Lectures On Political Economy (vol-i)

LECTURES ON

POLITICAL ECONOMY

By

KNUT WriCKSELL

TRANSLATED FROM THE SWEDISH BY

E. CLASSEN

AND EDITED WITH AN INTRODUCTION BY

LIONEL ROBBINS

Professor of EcoTiomics in the University of London

Volume One

GENERAL THEORY

London :

GEORGE ROUTLEDGE AND SONS, LTD.

Broadway House, 68-74 Carter Lane, EC.

Fir'll Published. Ma\ Pi.il-
Reprinted. Ma\ 19^5.
Reprinted, Augi.st 1938
Reprinted. Febniar\ 19t6

P R I N T f* D IN G R L A 1' BRITAIN BY
LLND HUMPHRIES
I. O N D O N

BRADFORD

CONTENTS OF VOLUME I

PAGE

Introbuction by Professor Lionel Robbins vii

Author’s Preface to Second Edition xxi

INTRODUCTION 1

I. THE THEORY OF VALUE 13

1. Exchange Value and its Causes. Earlier Explanations 15

2. The Concept of IMarginal Utility 29

3. Free Exchange and Market Value 35

{a) The different uses of a single commodity 35

(5) Exchange at given prices 43

(c) Isolated exchange 49

{d) Price formation in the open market. Exchange of two

commodities 52

(e) Continuation. Exchange of three or more commodities 63

4. Objections against the Theory of MLarginal Utility.

Exceptions to the Theory 68

6. The Gain from Free Exchange 72

6. Pricing under Limited Competition 83

{a) Joint Supply and Joint Demand 83

(6) Pricing in Retail Trade 86

(c) Monopoly Prices 88

7. Pricing under the Influence of Production 97

II. THE THEORY OF PRODUCTION AND DISTRIBUTION 101
1. Production without Capital 108

(a) Landowners as entrepreneurs 110

(b) The labourer (or a third party) as entrepreneur. The

profits of the entrepreneur 124

(c) The influence of technical inventions on rent and wages 133

CONTENTS

PAGE

2. CapitaIiIStic Peoduction 144

(a) The concept of capital 144

(b) The marginal productivity of capital. Capital investment

for a single year 147

(c) Capital investment over a period of years 15?

Note on Bohm-BawerFs Theory of Interest 167

(d) Alternative treatment of the problems of interest and

distribution 172

(e) Controvemies concerning the theory of capital 185

3. Tsb Interdependence op Production and Exchange.

The Theory op Exchange- value in its Final Form 196

III. CAPITAL ACCUMULATION 207

APPENDICES 219

1. Peopessob Cassel’s System of Economics 219

2. Real Capital and Interest 258

(a) Br. Gustaf Akerman’s Realhapital und Kapitalzins 258

(b) A mathematical analysis of Br. Akerman’s problem 274

INTRODUCTION

Johan Gustaf Knnt Wicksell, the author of these lectures,
is an economist of outstanding achievement whose work has
not yet received in English-speaking countries the attention it
deserves. In Scandinavia where he taught, and in Central
Europe and Italy where he has long been read, his influence has
. already been extensive and important. But, in other parts,
even at the time of his death in 1926, he was probably less
known than any other economist of commensurate rank. In
recent years, however, largely as a result of the writings of
Professor Hayek and Mr. J. M. Keynes, his theories concerning
the rate of interest and the price level have become more widely
known and his reputation is on the increase. It is safe to say
that as the main body of his work becomes available this process
is likely to continue.

Wicksell was born in 1851. He was thus nine years younger
than Marshall, three years younger than Pareto, and the exact
contemporary of Bohm-Bawerk and Wieser. His interest in
Economics developed comparatively late : his first important
work, Uber Wert, Kapital und Berde, was not published until
1893. He graduated in philosophy and mathematics, and it was
not until after taking his second degree in 1885 that he turned
his attention seriously to the subject which became his life-work.
After ten years’ further study in France, Germany, Austria, and
England he took his doctorate in economics. In 1900 he was
appointed assistant professor of Political Economy at Lund.
From 1904 to 1916 he held the chair in the same university.
He died in 1926.

^ In preparing this introduction I have been greatly helped by articles
dealing with Wicksell and his work by Professors OhUn and Somarin, which
appeared in the Economic Journal, vol. xxxvi, p. 503 seq., and the Zeitschnft
fur Nationaldkonomie, Bd. ii, S. 221 seq., respectively. A succinct and well-
documented account of WickseE’s work on the theory of Money and Capital
and its influence on certain contemporary writers is to be found in an m yet
unpublished thesis submitted by Mr. Solomon Adler to the University of
London for the degree of M.Sc. (Econ.) in 1932, and a useful discussion of
parts of this theory is to be found in l^chmann, SPudien mir Ormzproduk-
HvUatsiheorie dea Ka^pUahinaes,

viii INTRODUCTION

Wicksell s central contributions to theoretical economics are
all outlined, if not fully developed, in three books, all in German,
which appeared in rapid succession at the commencement of
his career in the nineties : tJhef Wcft, Kdpital und Rente, which
appeared in 1893 ^ ; FinanztJieoretische Untersuckungen, which
appeared in 1896 ; and GeUzins und Guterpreise, which appeared
in 1898. In the first he developed an outline solution of the
main problems of the pure theory of value and distribution.
In the second he applied certain elements in this solution to
the special problems of the theory of public finance and the
incidence of taxation. In the third he developed his now cele-
brated theory concerning the relationship between the money
rate of interest and the general level of prices. His Vorlesungen
uber NatimaloJcononm, of which the present volumes are a
translation, were published first in Sweden in two parts, General
Theory, and Money and Credit, in 1901 and 1906 respectively,
and contain, with much new material, a systematic restatement
of the main theorems of the first and the third of these earlier
treatises.

It would be a great mistake, however, to regard WickselFs
work as an economist as limited to these four major publications.
He published much on the population problem, played an
active part in the discussion of public aflfairs in Sweden, and
tliroughout his career was a regular contributor to the scientific
journals in Sweden and elsewhere. The files of the Ekonomish
Ttdskrift are full of lengthy articles by Wicksell, tantalizingly
inaccessible to those of us who have not the good fortune to
possess a sufficient knowledge of Swedish.^ The German
periodicals contain a number of contributions, and the Economic
J mimdl and the Qmrterly J ournal of Economics, once at least,
each secured an important article from his pen.^ Few economists

1 Some of the matter included in this book had been published in
Conrad' & J ahrbilohtr in the preceding year.

® Some of these contributions are now available in one or other of the world
towages. The article on Profe^or Bowley’s Mathematical Economics, with
ite discussion of the theory of* Bilateral Monopoly, appears m the Archw fur
^oz»a?«?is^e?wfcAa/^,Bd.58,pp.252-281. Professor Hayek has included a celebrated
article on Pn^s and the Exchanges in his Beilrage zur Qeldtheone, and two
o&w on Dr. Gustav Akermann’s BealJcapUal urtd Kapitalzins and Prof. CasseFs
peoiy of Social Economy ” appear in English as appendices to the present
volume. But an English translation of a comprehensive selection of these papers
18 still urgently to be desired. ^ ^

® A short list ot Wicksell’s principal contributions to foreign periodicals is
given by Professor Ohlin, op. dt., p. 512.

INTRODUCTION

IX

of Ms generation were more productive or — ^if those articles
wMch are accessible in one or other of the world languages are
any criterion — ^maintained so consistently Mgh a level.

It is not easy in a few paragraphs to give a just view of the
place in the Mstory of modern economic theory of Wicksell’s
main achievements. As we have seen, he was the contemporary
of men like Bohm-Bawerk and Pareto, whose work falls naturally
under the headings appropriate to the so-called Schools — the
School of Vienna, the School of Lausanne, the School of Marshall.
But Wicksell fits into no such classification. No economist
of similar rank has been more open to outside influences. But
the influences were not all from one quarter. From the outset
of his work in the nineties, he stands apart from the disputes of
the Schools, deriving equally from the good elements in each
of them — a pioneer of a generation wMch stands beyond these
early factions and can perceive both the common denominator
and the particular contribution in their respective systems.
There is no economist whose work more strongly exemplifies
both the element of continuity and the element of progress in
the central tradition of theoretical Economics. Few have known
better the works of the English classics or used them to greater
advantage. To those brought up in the English tradition of
post-classical Ricardian criticism his lucid reformulations of
their doctrines must come as something of a revelation.. But
his debt to the later schools is no less evident. In the broad
outlmes of his value theory, the Austrian influence is strong ;
and in Ms capital theory the influence of Bohm-Bawerk is obvious.
But the whole is set in a framework wMch derives essentially
from Walras, and the detail owes not a little to Wicksteed and
to Edgeworth. In short, in spite of his dates, Wicksell is of the
present generation.

In all tMs, of course, he bears a strong resemblance to Edge-
worth, our own great eclectic. There are indeed many elements
in common in their work. Many of the problems which interested
them were the same — distribution, public finance, the theory
of monopoly — and they both brought to their solution that
essential seriousness characteristic of those who are conscious
of working with the instruments of an established scientific
technique. But there was this important difference. Whereas
Edgeworth’s eclecticism showed itself mainly in the analysis

X

INTRODUCTION

of particular problems, Wicksell’s stowed itself even more
strongly in a tendency to synthesis. His particular investigations
are important. But even more important are his reconstructions
of general theory. He had the feeling for broad effects, the
capacity for wide abstraction of the great system-makers. * But
being a scientist and not a mere system-maker, the system he
constructed was not specifically his own but the system common
to the best work of the past hundred years of economic theory.

In this respect, perhaps, he is more to be compared with
Marshall, and more than one critic has made the comparison.^
But here, too, there are important differences. There can be
little doubt that in general knowledge of the details of economic
relationships in the modem world, Marshall was greatly WickselFs
superior, as indeed he was the superior of most others of his
generation. But as a systematizer of pure theory he had the
defects of his qualities. The peculiar blend of realistic knowledge
and theoretical insight which enabled him to present with such
ingenuity the world as he saw it, was not necessarily conducive
to clear presentation of abstract theoretical issues. He was
so anxious to explain the reality he knew, to make his theory
appear plausible, that he was apt to be impatient with refine-
ments which, though useless for this purpose, might be fruitful
in other connections. Moreover, as Mr. Keynes has pointed out,
he lacked that aesthetic feeling for order and proportion which
is essential to a theoretical synthesis on the grandest scale.
It was just here that Wicksell excelled. There is no work in the
whole range of modem economic literature which presents a
clearer general view of the main significance and interrelations
of the central propositions of economic analysis than these
lectures. The arrangement is exemplary. The successive pro-
positions are presented in a setting which emphasizes both their
implications and — ^what is just as important—their limitations :
and the whole is bmlt up in such a way that at each successive
point in the argument attention is always focused upon the
new elements in the problem, the rest having been satisfactorily
disposed of at an earlier stage. In this no doubt Wicksell learnt
much from Walras. But no^ one would contend that the
exposition of the EUmeuls WEconomie Politique Pure, littered

Bd ** Knut Wicksell,” Archiv fUr SozicdmssmscTuift,

INTRODUCTION

XI

up as it is with, so much superfluous and somewhat crude
mathematics, is a model of expository clarity.

In certain respects, the closest comparison is with Wicksteed.
For Wicksteed had the architechtonic instinct, and he, too, had
derived both from Lausanne and Vienna. He had not, however,
Wicksell’s feeling for the English classics, and the development
of his thought was on different lines. Strongly influenced by
Pareto’s modifications of utility theory, in later years he became
more and more interested in the philosophical and methodological
implications of the general theory of value. Wicksell, on the
other hand, who was a bit "old fashioned on pure utility theory,
turned his attention more and more to the development of
that part of the Jevonian-Bohm-Bawerkian theory of capital,
which, just because he rejected the classical writers so completely,
in certain respects Wicksteed failed to comprehend ^ ; and as
time went on his interests became more technical and practical.
But the two supplement each other in admirable fashion. The
subjective side of modem theory is at its best in Wicksteed,
the objective in Wicksell ; a combination of the two covers much
of the essential ground.^ I am not clear that Wicksteed was
acquainted with Wicksell.^ But there is ample evidence that
WickseU knew Wicksteed’s work and appreciated it long before
much was thought of it in England.

Any enumeration of Wicksell’smore outstanding contributions
to the detail of Economic Science must commence, if it is to do
justice to his own wishes, with his contributions to the theory
of population. It was the reproach that his knowledge of the
economics of the population problem was insufficient, which
first directed his attention to scientific economics ; and thoughout
his life, the population problem in all its aspects retained the

^ In this connection a comparison between Wicksteed’s article on Jevons’
“ Theory of Political Economy ” {Works, vol. li, pp. 734-754) and the section son
Capital Theory m Uber Wert, Kapital und Rente is very mstructive.

^ But not all. I should be very sorry to be thought to lend any countenance
to the view, now apparently gammg ground m somewhat unexpected quarters,
that m undergraduate teachmg or in advanced studies we are yet m a
position to dispense with the most thorough study of Marshall’s Frinciples,
It would be a sad thing if the uncritical acceptance of this great work,
which so long tended to stiffle the development of other Imes of thought
in this country, were to be succeeded by an equally uncntical rejection of
all the wisdom and the path-breaking mtuitions that it contams.

® He must have been aware of Uber Wert, Kapital und Rente, for it was
reviewed together with his own Co-ordination of the Laws of Distribution m
the Economic Journal for June, 1894.

xii INTRODUCTION

strongest told on tis interest and emotions, so muct so indeed
that in 1909 he incurred the penalty of a short term of imprison-
ment on account of strong utterances on certain of its non-
economic aspects — a period which he devoted to the preparation
of a short book on this subject signed defiantly '' Ystad Prison
In the statistical field, he did much important work on the
mechanics of population increase, and, in the field of economic
theory, he was one of the first systematically to develop the
concept of an optimum population. Whether it is so easy at
any time to assign a specific magnitude to this elusive concept
as Wicksell himself supposed, whether indeed we really yet
know enough about the application of the laws of returns in
this connection to be in a position to describe it in a way which is
theoretically satisfactory, are questions on which differences of
opinion between reasonable men may yet legitimately arise.
But the emphatic pronouncements in the introduction to the
L^ures on the place of population theory in a systematic
treatment of economic problems are a sufficient indication of the
importance Wicksell himself attached to this part of his work.

To the broad outlines of the theory of value Wicksell added
little that was completely original. But he fused the main
teachings of Walras and the early Austrians with great
ingenuity and expository powder, giving to the philosophical
insight and profoundity of Menger and his followers, the
superior precision and elegance of the mathematical formula-
tion. Seldom have the complications involved in the
transition from pure utility theory to the theory of exchange
and price been stated with greater clarity and exactitude.
To more recent developments of the theory of value he was
not very sympathetic, probably on account of the very strong
utilitarian bias in his general view of the subject. The student
of the theory of public finance, however, should not miss his
discussion of the principle of justice in taxation.^

In the theory of production Wicksell displays much greater
originality. His statement of the marginal productivity theory
is one of the most satisfactory available. As Dr. Hicks has
shown, ^ the exposition in the Lectures, with its express condition

^ Finamiheoreiische UnterawJmngen, p. 176 8eq. Wicksell’s views in this
spect have been developed with great ingenuity by his pupil, Prof^^sor
E. Lindahl, in his Die OerecMigkeU der Best&mrung,

2 Theory of Wages, p, 233.

INTEODUCTION

xiii

that the various firms concerned must be at a stage at which
father economies of large scale production are absent,
is immune from the strictures which have been passed by
Pareto, Edgeworth and others on the version which is to be
found in Wicksteed’s Co-ordination of the Laws of Distribution.
In this he may have been indebted to Walras. But in the light
of the discussion of the theory of distribution in liber Wert,
Kapital und Rente, Wicksell must himself be looked upon as
one of the founders of the marginal productivity theory.

Most conspicuous, however, in the sphere of the theory of
production is Wicksell’s contribution to that part which deals
with problems of capital and interest. Here his eclecticism rises
to the point of pure genius. By a judicious selection from the
best elements in earlier theories he achieved a reformulation
of this part of the theory of production from which, it is safe to
say, all future work in this field which aspires to be taken seriously .
must commence. It is worth examining the nature of this
achievement in rather more detail.

The part played in the classical system by the ingredients
of a substantially correct theory of capital and interest is by no
means so negligible as post-classical criticism has often assumed.
On the one hand in the wage fund theory, on the other in the
Ricardian modifications of the labour theory of value, particu-
larly in the letters to McCulloch, there exist the rudiments of a
theory in many essential respects not dissimilar from that which is
to be found in Jevons, Bohm-Bawerk and Wicksell. In a series
of brilliant reconstructions in the Finanztheoretische Unter-
suchungen and elsewhere, Wicksell himself indicated the
significance of certain aspects of the classical doctrines in this
respect. More recently Mr. Edelberg has shown ^ how, if one is
willing to give Ricardo the benefit of the doubt in one or two
connections, a whole theory of capital and interest on WickseUian
lines can be reconstructed from actual Ricardian material.
In any case it cannot be said that important theories of capital
and interest played a negligible part in the classical system.
Indeed, if a choice had to be made between the classical theories
and those modem systems which ignore the Jevonian-Bohm-
Bawerkian reconstruction and reject the classical elements,

^ “ The Ricardian Theory of Profits,” EcoThomica, February, 1933,
pp. 51-74.

XIV

INTKODUCTION

there is mtich to be said for the view that the classical theories
would be much less likely to mislead.

But the classical system as a whole was very vulnerable.
It was open to general attack on its theory of value. It was
everywhere deficient on points of formulation. And these
particular theories of capital and interest were liable to attack,
not merely for their obvious deficiencies in this respect, but also
for political reasons. As time went on, the wage fund doctrine
in particular, instead of being reformulated in those minor respects
in which it was defective, became the target of continuous and
completely hostile criticism, some of it justified in points of
detail, but most of it analytically erroneous and totally beside
the point. Nothing could be more superficial — ^for instance —
than the criticisms put forward by writers such as Walker
and J. B. Clark of the incontrovertible proposition that wages
, are paid out of capital. But for political reasons the classical
theories of capital were unpopular and men jumped at any
pretext for rejecting them. The result was that, particularly
in English circles, much of the Economics of the fifty years after
x870 was what Wicksell calls a KapUallose Wirtsckaftstheorie
— an economic theory of acapitalistic production. Considerations
of capital theory proper, save of a more or less terminological
nature, simply disappear from the picture. Professor Taussig’s
Wages and Captial was a gallant attempt to stem the tide —
which incidentally carried through most of the modifications
necessary to make the classical theory logically acceptable and
completely disposed of the ridiculous myth that it had originated
in selfishness and reaction. But it was in vain. When, after
the war, Mr. Dennis Robertson and Mr. J, M. Keynes turned
their attention to problems of fluctuation which involved similar
considerations, the tradition of a theory of capital had so
completely disappeared in English Political Economy that they
had to start completely from the beginning. Nor was the
position any better in certain continental circles. The work
of Pareto, valuable as it is in other respects, adds little to
kno'w ledge in this connection. It would perhaps be putting
it too strongly to say that there is no capital in his equations
of economic equiHbrium. But it would certainly be correct
to say that there is no time. Now time is the essence of capital
theory.

INTRODUCTION

XV

There was another stream of thought, however, in which the
theorems of the classical economists were by no means altogether
abandoned. In spite of his antipathy for Mill and his celebrated
denunciation of his four fundamental propositions on capital ''
— “all wrong,” as he said, Jevons had taken over into his capital
theory important classical elements. And in Bohm-Bawerk's
“ Positive Theory of Capital ” something very like the classical
wage fund theory, shorn of its obvious defects of formulation,
makes its appearance. But Jevons’ chapter on capital was only
an outline ; and, for various reasons, the influence of Bohm-Bawerk
was not altogether fortunate. In his critical work, he was
undoubtedly unjust to many of his predecessors. This, where
it did not create repulsion, created the impression of a much
greater lack of continuity than actually existed. And in his
positive solution, which in most important respects was sub-
stantially correct, the emphasis and arrangement was such as
to make understanding of the main elements much more difficult
than need have been the case. The sections dealing with the
element of time discount are admirably clear and have made a
permanent mark on the discussion of the subject elsewhere.
But the sections relating to the “ third ground ” for the existence
of interest — ^the “ technical superiority of present goods ” — are
developed in a mode which definitely invites criticism. What,
as Wicksell points out, is really the central and fundamentally
unassailable core of the Bohm-Bawerkian theory — ^the discussion
of the influence of the varying productivity of productive
processes of different lengths on prices, the use of the subsistence
fund, and the formation of the rate of interest — only appears
as a sort of practical application of these more disputable
propositions at the very end-of the book. It is clear that many
of Bohm’s readers never reach that last section. The result has
been that in those parts where the oral tradition of Bohm-
Bawerk’s seminar was not influential, it came to be thought
that the theory of the relation of time discount to interest was
Bbhm-Bawerk’s chief contribution. The propositions relating
to the “ third ground ” were held to have been disposed of by
the criticisms of Professors Fetter and Fisher ; and the most
valuable element in the solution, therefore, what is really a
marginal productivity theory of interest, properly stated in
regard to the time element, tended to escape attention.

INTRODUCTION

xvi

But not with WickselL For Wicksell the productivity side
of the question was obviously at once the more important
and the more deserving of further elucidation. Steeped as he
was in the literature of the classical system, he had no difficulty
in detecting the underlying continuity between Bohm-
Bawerk’s theory of the subsistence fund and the classical
wage fund theory, and with his mathematical insight he
divined, in spite of all Bohm-Bawerk's disclaimers, the
substantial identity between the general marginal productivity
analysis and the propositions relating to the varying produc-
tivity of different investment periods. He was thus able
to present an account of equilibrium of capitalistic production
which combined all the best features of these apparently divergent
theories, and, by invoking the methods of Walrasian analysis,
he was able to present it in a much more general setting than
was the case with either Jevons or Bohm-Bawerk. It is true that
this theory itself is not complete. It was fully developed in the
Lectures only 'for the case of circulating capital. And although
later on, m his review of Dr. Akerman’s book (printed below as
Appendix 2) Wicksell developed a solution for the case of capital
of varying degrees of durability, it is obvious that this is one of
the fields of pure analysis in which most yet remains to be done.
But the fundamental ideas of his theory — the place of the varying
productivity of variations in the investment period, the idea
of interest as the difference between the marginal productivity
of direct and indirect uses of factors of production — these
are notions which are not likely to be superseded and which are
fundamental as a basis for future work.

I come finally to what is probably the best known of WickseU’s
contributions — ^his celebrated theory concerning the relations
between money and natural rates of interest and movements
in the general level of prices. This is probably Wicksell’s most
original contribution. The main propositions are certainly
not new. As Professor Hayek has shown ^ there is a very
considerable body of passages in the classical literature, in which,
in one form or another, they make their appearance. But,
apart from one isolated passage in Ricardo, which Wicksell

and Production, chapter i, passim, « A Note on the Development of
pp J^orced Savmg,»” QuaHerly Journal of Economics, vol. xlvii.

INTRODUCTION

xvu

says explicitly was only brought to his notice after the publication
of his own theory, these passages are not in the most conspicuous
or most easily accessible works, and there seems little reason
to question that, in so far as any idea implicit in the fundamental
notions of Economics can be so described, his main idea was
original.

Its influence has been far reaching. It is clear that in WickselFs
own treatment, in certain respects — not unimportant in regard to
practical applications — ^it is not correctly developed. It can be
shown that the proposition that the money rate of interest
which keeps prices stable is also the rate which clears the market
of voluntarily accumulated capital, breaks down when the
conditions of capital supply are either progressive or retro-
gressive.^ It is clear that it stands in much need of refinement
before it can be applied to the interpretation of actual conditions —
still more as a guide to practice. The notion of a single rate, either
natural or monetary, needs to be replaced by the idea of a
structure of rates ; and the interrelations of these rates, and their
relation, not merely to the stream of saving, but also to the risk
factor, need much more study. But when aU is said by way of
qualification, it remains true that the discovery, or rather the
rediscovery, of the general relationship involved is one of
the greatest single steps forward in monetary economics since
the proper elaboration of the quantity theory. It is the key,
not only to the more complex problems of fluctuations of
monetary value, but also to much that is central in the general
theory of capital and the theory of business cycles.
Monetary theory and capital theory alike are at an impasse
when the theory of money is limited to the simple quantity
theory and the theory of capital is divorced from the theory
of the money market. The value of money is said to depend
on the quantity of money and the velocity of circulation, the
rate of interest on the marginal productivity of extensions of
the investment period, and the rate of time discount. The
relations between the supply of capital and the supply of money,
between the money rate of interest and the rates of real accumu-
lation and investment, not to mention the relations between

^ See Hayek, Monetary Theory and the Trade Cycle, chapter v, and Prices
and Production^ chapter i ; also G. Myrdal, “ Der Gleichgewichtsbegriff als
Instrument der Geldtheoretischen Analyse,” in Beitrage zur Geldtheorie, ed.
Hayek.

b

xviii INTRODUCTION

relative prices at various stages of production and tlie rate of
borrowing of the entrepreneurs — all these problems, whose
solution is essential to any comprehensive theory of economic
change, remain unexplained until this fundamental conjunction
has been ejBfected. No doubt in this field it has been left for
others to develop the implications of the broad principles wljich
Wicksell laid down and even now much work still remains to
be done. But the main credit of rediscovering these principles
and bringing them once more into the centre of discussion must
rest permanently with the author of these lectures.

The present translation is based upon the third edition,
published in Sweden after the death of the author under the
editomhip of Professor Somarin. The two volumes into which
it is divided, which deal with general theory and money and
credit respectively, are to be published successively and will be
sold separately. There have been added, as Appendices to
Volume I, two of WickseU’s longer articles, one which adds to
the capital theory of Book II further elucidations of the problem
of durable capital not provided in the text, and another, which,
in the form of a lengthy critique of Professor CassePs Theory of
Social Economy, underlines various details of Wicksell’s general
outlook. The inclusion of this latter must not be thought to
imply any special endorsement by the editor of all the
various criticisms it contains ; there are, indeed, several not
unimportant points, notably those relating to the measurability
of utility, where Professor Cassel still seems to me to have the
better of the argument. But it is always good to know exactly
where important authorities differ, and it was thought that
anything which should elucidate the relationship of the theoretical
systems of the two most famous Scandinavian economists of
our time would therefore be helpful.

Wicksell’s aim in preparing the Lectures was to provide a
work which would not only enlighten the professional economist
but would also serve as a textbook for students. It is with
this end in view that the present edition has been prepared.
It is not perhaps suited as an introduction for very young
students who have no preliminary acquaintance with economics
or any of the natural sciences. For such, some such work as

INTRODUCTION

XIX

Volume I of Wicksteed’s Commonsense of Political Economy is to
be preferred. But for more advanced students (i.e. students in
the first year of preparation for the final examination, as
distinct from students preparing for the intermediate) and for
readers of maturity it is admirably fitted for use as a general
textbook. I know no single work better suited to the needs of
any natural scientist who wishes to get a general view
of what theoretical economics is about, and to what extent
it is scientifically respectable. In parts the exposition is
mathematical. But here, as in the original, the more advanced
sections and the sections involving calculus have been printed
in smaller type and may be omitted on first reading. The
main argument throughout is accessible to those who have no
mathematical competence.

The task of editing the translation of a technical work of
this sort is always somewhat arduous, and I am indebted to
many friends at the London School of Economics who have
lent assistance. The ‘final version of the text owes much to
Dr. J. R. Hicks, who generously gave much time to the checking
and correction of the manuscript. In addition to providing the
translation of the Appendices, Mr. Solomon Adler gave valuable
assistance and advice concerning the rendering of technicalities,
and Mr. E. S. Tucker has borne the main burden of the laborious
task of seeing the book through the press.

Lionel Robbins.

London School of Economics.

April, 1934,

FROM THE AUTHOR’S PREFACE TO THE
SECOND EDITION

The first edition of this book was a very limited one, for
I did not wish to deprive myself of the opportunity of publishing
a new edition and of availmg myself of the improvements which
experience and expert criticism might suggest. Unfortunately,
very little criticism, either public or private, has reached me ;
but during the ten years or more in which I have been teaching
I have naturally discovered various defects, which in this edition
I have endeavoured to correct. By omitting the chapter on the
theory of population, which was published a couple of years ago
in a revised form as a Verdandi ’’ publication, it has been
possible, without increasing the size of the work, to find space
for certain additions, which, I hope, will increase its value and
its usefulness. Thus the presentation of the theory of rent and
the problem of distribution in a non-capitalistic economy has
been expanded and, in connection with the theory of interest,
some pages have been devoted to a resume and criticism of
Bohm-Bawerk’s theory in its original form. Similarly, I have
given a detailed alternative explanation ^ of the origin of interest
and of the solution of the problem of distribution under capitalistic
production, in which I assume that the whole of the available
supply of current labour and land is either invested in production
at once, at the same time, or possibly at different moments of
time ; after which, the products mature spontaneously under
the influence of free natural forces — ^as for instance in the
laying down of wine for consumption, etc. Interest then appears
in its purest form as the ‘‘marginal productivity of waiting’'
(or of time), and the problem, in all its phases, is easily susceptible
of exact treatment in a mathematical form, without it being

^ This expression is perhaps not entirely suitable, since, as will easily
be seen, the essence of the argument is in both cases the same. It is therefore
also possible that I ought to have endeavoured to combine sections II, 2, C
and 1) in a single uniform presentation. I have found myself unable,
however, for various reasons, to do this. As they now stand, these two collateral
presentations may materially support and explain each other.

xxi

XXll

from the AUTHOR’S PREFACE

necessary to have recourse to calciilation with so-called simple
interest, as in Bohm-Bawerk’s well-known exposition.

Finally, the original brief discussion of the phenomena of
the accnmnlation of capital has been expanded, and now includes
an examination of Professor CasseFs interesting contributions to
the still very meagre literature of this subject.

As will appear from what has been said, the present edition
has a more mathematical ” character than its predecessor.
In every case, however, I have prefaced the mathematical
analysis by an elementary treatment with definite — ^though
usually arbitrary— figures. The passages in smaller type can,
for the most part, be read and understood without any special
knowledge of mathematics, and for the remainder, as I have
said in the text, the standard reached nowadays in secondary
schools should suffice.

Opinions may differ as to the value of this method. For my
own part, I am convinced that a constant and logical argument
from simple assumptions conveys more real knowledge than
variegated but superficial talk upon everything under the sun :
national character, racial differences, will to power, class interests,
etc. Again, as regards the controversy concerning the so-called
historical and theoretical treatment of economics (of which the
latter must of necessity be more or less mathematical), this is
a matter which can, in my opinion, be settled only by a division
of labour. We must be deeply grateful to those persons who, by
the discovery and investigation of documents relating to economic
history— matters treated in a very stepmotherly fashion by
earlier historians — ^have succeeded in illuminating the present by
the light of the past, and in showing to us some links on a chain
of development of which we ourselves and our environment
constitute another link. But, on the other hand, if economics
is some day to become a real science and guide to practical
business it must inevitably advance to certain positive results
and principles of universal application. It will not do to treat
questions relating to economic policy, to trade and industry,
and esj^cially to population, as if they were metaphysical
speculations in which each person can adopt the point of view
which appeals most to his temperament — and still more
frequently, ^rhaps, to his private interests. We are here
concerned with substantial quantities, measurable magnitudes,

FEOM THE AUTHOR’S PREFACE xxiii

a and 6, plus and minus. To secure an explanation of tteir
relations wMcli would be convincing to every thinking and
unprejudiced person cannot be said to be outside the scope
of economic inquiry, but must, on the contrary, be its
ultimate goal.

,I am, of course, far from regarding the following arguments,
which are for the most part hypothetical, as an adequate
foundation for a practical treatment of economic questions,
though I have little doubt that they constitute a necessary
preliminary — ^and, at the same time, provide a useful exercise
for those concerned with such problems. In more than one
case it may appear that a direct application of our principles
to actual politico-economic problems would be quite natural.
In such cases we must certainly be on our guard against
over-hasty generalizations from results achieved by way of
abstract deductions ; and, unfortunately, the mathematical
method affords no absolute guarantee against false deductions.
But, in any case, that method has a great advantage over the
merely descriptive method, in that errors committed cannot
long be concealed, and false opinions cannot be defended long
after they have been shown to be wrong.

E[nut Wicksell.

Lmm.

March, 1911 .

LECTURES ON POLITICAL ECONOMY

GENERAL THEORY

INTRODUCTION

THE NATURE OF ECONOMICS : DIVISION OF THE SUBJECT

It is not easy to give a satisfactory definition of the term
‘‘ political economy The conception itself is, indeed,
somewhat vague — a natural state of affairs in the infancy
of a science. Literally, the name indicates national house-
keeping or the theory of national housekeeping. Yet,
at any rate nowadays, a nation has no common housekeeping,
but every individual manages his own affairs. The State itself
constitutes a management of some affairs in common and the
same is true of the local units ; the housekeeping of those units
is dealt with by the science of public finance, which, though
it must be regarded as a part (and an important part) of political
economy, is by no means the whole. In modern times, moreover,
it has become customary to treat public finance as a distinct
science.

The name political economy arose during the so-called
‘‘ mercantile ” age, when it was regarded as a duty of the State
itself to exercise an extensive influence over the aJlairs of
individuals, so that the latter enjoyed only a very restricted
liberty, under the guidance and control of the State. At that
time, therefore, it was appropriate to speak of political economy,
a term which adequately represented the conception which
underlay it. Its appropriateness diminished with the advent of
the physiocratic ideas and the victory of the conception of
unrestricted liberty and free trade, especially as the main thesis
of the latter was that the State should interfere as little as
possible in economic affairs and leave the individual, except
in certain well-defined cases, free to attend to his own business.

[Swedish Naitoiwlekonomit German NtUwnaldIconomie.']

2 LECTTIBES ON POLITICAL ECONOMY

Thus, according to this view, the fundamental principle of
political economy was that its subject matter, the national

tonselioM, did not exist.

In our day, it is true, there has been a reaction against
this ultra-liberal principle, but nevertheless it is still in reality
the individualistic, purely private, system which predominates.
For this reason many modern writers have desired to reject
the qualifying adjective ‘‘ political or national ” and to speak
merely of economics, or have invented entirely new names, such
as plutology ’’ or ‘^catallactics”. But in the absence of
a better name we may perhaps retain the old one,^ provided
that we are careful not to import into it the conception of
a national unity in the economic field which does not exist in
reality. In accordance with the modern outlook, the subject
matter of , political economy is becoming more and more the
doctrine of economic phenomena, in their interrelations, seen
as a whole ; i.e. in so far as they uniformly afiect whole classes
of the community, or a whole people, or the totality of all
peoples (what the Germans call WeUwirtsckaft). By an economic
phenomenon or activity is meant every systematic endeavour
to satisfy a material need, or, more precisely, one which seeks
with the available means to achieve the greatest possible result,
or a given result with the least possible means. (The famihar
expression, “to obtain the greatest possible results with the
smallest possible means,” is illogical and should therefore be
avoided.)

In many cases such an activity, though directed to the
advantage of an individual, at the same time promotes, or is
at least not inimical to, the general good. He who works and
produces only for his own gam also confers benefits on others
— ^indirectly, by means of exchange) the improvement of the
soil and of technical plant in general, which is effected by the
present generation, possibly only in its own interests, will,
nevertheless, be of benefit to the coming generation. In such
cases individual and national economic interests coincide. But
it is equally common, or even more common, for one economic
interest to conflict with another j circumstances or activities
which benefit one branch of industry, one class of society, or
one generation, are often more or less injurious to another.

^ [i.e. NcUioTialehonomi (Swedish) or NationdlokoTiomie (German).]

INTRODUCTION

3

Examples of tMs kind are familiar to everybody ; the most
important is surely the distribution of property, in so far as
possession of land or an exceptional monopoly of any kind
necessarily excludes others from that land or that monopoly.
Private and national economic interest then no longer coincide,
and the question arises which is to be followed ; in other words,
which of two conflicting interests is to be preferred as contributing
most to the general good. To answer this question is the practical
and social duty of political economy, and it might be said that
the definition of political economy as a practical science is the
theory of the manner of satisfying human needs which gives
the greatest possible satisfaction to society as a whole, ^ having
regard to future generations as well as to the present. The
existing individualistic organization of society, in so far as it is
socially justified, must then be regarded as a means to the
attainment of that end.

The solution of this problem is frequently very difficult
and the result is, of course, alwaj^ dependent not only on
technical economic considerations, but also on the degree of
our sympathies ; that is to say, on our understanding of the
interests and demands of others. When we say that a thing
is beneficial or injurious from the point of view of political
economy, this maimer of speaking is based on an ethical or
philosophical postulate ; that is to say, on certain conceptions
concerning the natural right of men to live and enjoy the good
things of life. We either consider all to have the same rights
and reckon each individual member of society as a unit, or
else, for one reason or another, we recognize a difference between
them, though in that case the reasons must be clearly stated
if we are to regard our view as scientifically established.

As we all know, opinions on this question have changed
greatly in the course of time. In earlier times, only the free, and
afterwards only the propertied, classes were regarded as members
of society in the true sense ; slaves and those without property
were regarded in much the same way as domestic animals in
our day — merely as a means and not as an end. Aristotle’s
well-known saying that shuttles and the plectron of the lyre
would have to move of themselves before slavery could cease,

^ Here, too, one should avoid the very common, but fundamentally
meaningless, expression “ the greatest happmess of the greatest number

4

LECTUEIS ON POLITICAL ECONOMY

is evidence of tMs view, ttongli we need not go back so far
in time to encomiter similar opinions. Among eighteentb century
Swedisb writers on economics, mentioned by Amberg in bis
Ffihdsiidem politiska ekonomi The Political Economy of the
Age of Freedom”),^ we repeatedly find remarks which show
that the conception, so repellent to our m inds, of a workman
as a mere beast of burden was, as recently as two centuries ago,
stni general and deep-rooted. Indeed, it may be regarded in
some degree as one of the merits of economic science that in
this respect it has produced a revolution in pubhc opinion.
As soon as we begin seriously to regard economic phenomena
as a whole and to seek for the conditions of the welfare of the
whole, consideration for the interests of the proletariat must
emerge ; and from thence to the proclamation of eqml rights
for aU is only a short step.

The very concept of political economy, therefore, or the
existence of a science with such a name, implies, strictly speaking,
a thoroughly revolutionary programme. It is not surprising
that the concept is vague, for that often happens with
a revolutionary programme. Indeed, many practical and
theoretical problems remain to be solved before the goal of
economic or social development can be said to be clearly
understood. Something can still be said in favour of the older
point of view, but in any case it should be said straightforwardly
and without prevarication. If, for example, we regard the
working classes as beings of a lower type, or if, without going
so far as this, we regard them as not yet being ready for a full
share in the product of society, then we should say so clearly
and base our further reasoning upon that opinion. There is
only one thing which is unworthy of science—to conceal or
pervert the truth ; that is to say, in this case, to represent the
position as if those classes had already received all they could
re isonably wish or expect, or to rely upon unfounded, optimistic
beliefs that economic developments in themselves tend to the
greatest possible satisfaction of all. This latter mistake was
made especially by the so-called harmony economists in the
middle of the last century— the American, Carey, and the
otherwise admirable Frenchman, Bastiat— both of whom in

*friheutidens rtationaUkonomiska litteratur.

mTEODUCTION 5

their own countries and in ours have bad, and still have, many
disciples.

The division of the subject which first suggests itself is
into theoretical ’’ and “ practical political economy —
economics in the narrow sense and national economic policy.
Owing to the decisive dijfference which it makes to our handling
’ of economic problems whether we assume the existence of
private property and freedom of contract in anything like their
present forms, or whether we do not, it might be more appropriate
to subdivide the practical portion into two parts ; one being an
application of the theory /ownded on existing conditions, and the
other a critical examination of the foundation itself.

The former of these would be, at the same time, a link
betw^een the latter and the theoretical portion. On the one hand,
it amplifies the theoretical abstractions by a closer consideration
of reality, whilst, on the other hand, the practical problems
which emerge as soon as we approach reality can find their
ultimate solution only in a criticism of the foundations of the
whole economic life of society.

We thus arrive at the following division of our subject : —

(1) A theoretical fart (pure, general, or theoretical economics),
comprising a statement of economic laws or the connection
between economic phenomena, in which, in order to discover
or demonstrate these laws, we must necessarily proceed from
certain simplifying assumptions.

(2) A practical part (applied economics, particular problems
of the consumption, distribution and production of goods),
comprising the application of these laws to various fields of
activity in the concrete economic life of society.

(3) A social part (social economics or economic policy),
comprising an investigation into the question how these economic
laws and practical precepts should properly be applied in order
to obtain the greatest possible social gain, and what changes in
the existing economic and legal structure of society are necessary
to this end.

In the first of these main parts there are certain subdivisions.
First and foremost comes the theory of human wants, quantitative
and qualitative, i.e. the general theory of consumption, which,
smce it is the purpose of all economic activity, should logically
be placed first, even though in actual life it comes last in point

6 LlCTimES ON POLITICAL ECONOMY

of time. As regards sucli needs, or consumption, the q'mntitative
point of view emerges iBrst, and in this respect the number of
€X>iiBuiners is of decisive importance. Tims, in our first
subsection, we naturally treat of the theory of population, its
composition and changes. Man is, indeed, not only a consumer ;
he is also a producer. . Yet he is, both phylogenetically and
ontogenetically, both in racial and individual development,
a consumer long before he is a producer. In the theory of
production, moreover, man is only one of the productive factors ;
in the theory of consumption he and his purposes constitute the
whole. Generally speaking, and even apart from the above
division of the subject, it will be found that the theory of popula-
tion, which can never be omitted from a complete treatise on
political economy, can never find a suitable place in the system
unless it forms an introduction to the whole. In actual fact,
it is impossible to consider economic problems profitably, whether
they are of a practical or theoretical kind, unless we constantly
keep population and its changes in view. On the other hand,
it would appear that certain problems of population are of such
a complicated nature that they cannot be solved without
a thorough knowledge of every part of the theory of economic
structure. Thus we return to these problems at practically
every point in a thorough economic investigation, and their
solution may be regarded as its chief result.

We next turn to the qualitative side of human needs : to
their extent and mtensity, relative importance, etc., and the
comparative importance which we accordingly attribute to the
means of satisfying these needs. The development of this inquiry
will lead us to the theory of valice and to the associated general
theory of eaxtianqe. On the other hand, exchange as it appears
in reality in modem society, and the regulation of exchange
by society which may be considered desirable, belong respectively
to the second and third main sections of our subject.

The next subdivision is the general theory of production
and of the factors of production : land (or nature), labour, and
capital, their part in* production and their relative shares in the
distribution of the product — ^rent, wages, and interest — ^all
examined on certain simplif^g assumptions, such as universal
free competition or competition limited in a certain maimer.
It is already clear that the theory of production cannot be

INTEODUCTION

7

separated from the theory of distribidion^ though it should be
noted that this appKes only to distribution as it actually takes
place under the individualistic economic system, or, more
correctly, as it would take place on our simplifying assumptions.
The social problem of distribution, on the other hand, which
belongs to the third main division, is fundamentally different
from this ; it embraces, among other things, the question, not
yet raised at this stage, of property rights in the various factors
of production.

In these two subdivisions we shall treat the subject mainly
from the static point of view, i.e. we shall assume, in principle,
a society which retains unchanged from year to year the same
population, the same area of territory and the same amount of
capital, and remains on the same level of technical achievement.
By way of transition to a more dynamic point of view, which
can oiily be successfully presented in combination with the
practical part of our subject, we shall briefly treat the problem
of saving or accumulation of capital — ^which is equivalent to
production without corresponding consumption — as well as
its negative counterpart, capital consumption.

Finally, we include in the general or theoretical part of our
work the theory of the medium of exchange, money as well as
organized credit, which subjects are clearly connected and partly
coincide. Many monetary questions, it is true, have their proper
place in the special or applied section of our subject, but to avoid
unnecessary length we shall treat most of them together, more
especially since the actual technique of money is of much greater
interest to pure economic theory than the techmcal details of
production or trade.

We thus obtain the following five subdivisions of Part I of
our work : —

(i) The theory of population.^

(ii) The theory of value and exchange.

(iii) The theory of production and distribution.

(iv) The theory of capital, all of which are treated in
Volume I, and

(v) The theory of money and ctedit, which is the subject
of the second volume of the theoretical part of our work.

As I shall probably not be in a position to publish either

^ [For reasons explained in the author’s preface, this section was omitted in
the second Swedish edition and is not included in the present translation. |

8

LECTUEES ON POLITICAL ECONOMY

of the two other main parts, it is unnecessary to recount how
I have coBceived their content or how I have treated them in
my lectures. I need only add that the third mam division (or
Social Economics) would include, as its last section, a theory of
public finance — ^which is usually treated nowadays as a separate
science, as a study of particular financial legislation — ^thougji in
essence it undout>tedly constitu* es a part, growing more important
and extensive every day, of political economy.

This division of the subject accords in the main with that
used by Walras in his Mements d' economic politique pure^ though
it is not always based upon the same reasons. Formerly, following
the example of J. B. Say and J. S. Mill, it was usual to divide
economics into the theories of production, distribution, exchange,
and consumption — a chronological order, as it were, according
to which it was supposed that commodities must first be produced,
then distributed between the persons participating in the
production (workers, landlords, capitalists, etc.) and then
exchanged, in so far as they were unable to avail themselves
of their share in kind, and finally consumed. But this easy
division of the subject is far from logical. Production and
distribution cannot, as we have already pointed out, be
understood except in combination, and the concept of value
and exchange underlies both, a fact which has led to incessant
anticipations and circunolocutions unfortunate from an expository
pomt of view. And, again, there was not much left to say about
consumption when everything else had been treated ; so that
the whole of this section was completely ignored by Mill. Yet,
if this is allowed to happen, one loses sight of the fact that that
which directs — or, more correctly, ought to direct — all economic
activity is human needs. Thus the theory of wants or vcdue
should undoubtedly be placed first; and this is often done
nowadays, even by writers of textbooks who, like Professor C.
Gide, otherwise preserve the old division of the subject. On the
other hand, it can hardly be right to postpone discussion of
value, as Philippovich does, and only to treat of it in connection
with the theory of commercial practice. The theory of value
in its modem form has, as we shall see, been more or less
responsible for the transformation of every branch of political
economy and should, in combination with the theory of
population, constitute the foundation of the whole edifice.

INTRODUCTION

9

Anotlier consequence of tMs traditional division of the
subject has been that, within the various main divisions,
theoretical, practical, and social problems have been treated
together. At an earlier stage in the development of the science,
this might be defensible — ^and there is no doubt that it helped
to give to the works of MiU, as previously to those of Adam
Smith (whose division of the subject is somewhat different), a high
degree of literary charm. But in proportion as science develops
and becomes specialized, a different method becomes necessary
and, by adopting it, it becomes easier to escape the criticism,
advanced so often and with so much justice against the older
economists, that the range of validity of their conclusions was
not always clearly established.

It is a more especial disadvantage of the traditional division
of the subject that the theory of money came to be treated
as a mere episode in the theory of exchange, without regard to
its great theoretical and practical importance in every branch
of economics. This is probably the real reason why, despite the
voluminous writings on the technical aspects of money and
credit, no complete theory of money and its functions has ever
been advanced, and why it remains one of the least explored
fields in the theory of political economy.

Passing over to pure or theoretical economics (mth which
the present volume will be solely concerned) we should point
out that the exposition in the whole of this section must of
necessity be abstract and schematic ; the results will be
correspondingly hypothetical, that is to say, they can only claim
validity under our simplifying assumptions. Whether, and to
what extent, they will accord with reality will evidently depend
on two circumstances : first and foremost, whether our
assumptions are themselves founded on reality, i.e. contain at
least some elements of reality — ^which we must always demand,
for otherwise all reasoning about them would be sterile. We
can, for example, safely assume that men are actuated by
selfish motives, because that is always, at least to a very large
extent, true. But we can no more assume that they are filled
with a desire to injure each other than that they are purely
altruistic. Further, the conditions from which we abstract
must be relatively unessential, at least as regards the question
under discussion : when we are considering certain economic

10 LECTUEES ON POLITICAL ECONOMY

problemB such as, for example, price formation, we may forget
that man is not entirely individualistic but has also social
impulses. But we must not do so in other problems, as for
example in the politico-social field or in the science of public
finance. Having, by this means, obtained a first approximation,
it is possible by successive approximations (i.e. by taking into
consideration more and more of the conditions at first omitted)
to approach nearer and nearer to reality, in much the same way
as the astronomers were obliged to proceed in order to discover
the laws of the real movements of the planetary system.

It is not, however, always possible to decide in advance
whether the conditions from which we abstract are essential
or not. It may even happen that we must deliberately ignore
conditions which are in themselves of the greatest importance,
because the problem in question is of so complex a nature that
it cannot be rationally treated in any other way. Thus, in the
theory of value, we shall ignore, for the time being, the functions
of money — ^which in fact are essential and not merely of secondary
importance. And we shall often regard the economic activities
of a people as isolated, whereas among the peoples who interest
us, such an isolation does not, even approximately, exist and
therefore our assumption corresponds with reality only if we
look at the economic activities of the world as a whole. Similarly,
at the outset, we shall regard both exchange and production
as if each existed independently of the other, which is practically
never the case ; and, in the theory of production, we shall first
concern ourselves with non-capitalistic production, although
this bears no possible resemblance to actual production and,
strictly speaking, caimot exist in fact. In all these cases the
results are, of course, not even approximately correct, but are
purely hypothetical ; though the inquiry is not, on that account,
valueless. They constitute rather a necessary dement in the full
and correct solution of the problem under discussion and are,
therefore, to be regarded as useful work, even if it should
sometimes prove impossible, for the moment, to complete the
reasoning by the inclusion of other factors hitherto omitted.^

^ In the exact natural sciences, there are many parallel cases One of the
finest discovenes in hydrodynamics made it possible, by Green’s analysis, to
determine exactly the movement of a solid body of a hquid. Yet the formulae
so discovered do not (except superficially) correspond with observed facts,
because it was impossible to take certam important details mto consideration —

INTEODUCTION

11

It lias been customary in the so-called Hstorical scbool of ‘
political economy to deprecate all abstract reasoning within
the science as being useless. This view, which, however, seems
to be dying out, evidently disregards the fact that all human
thought, of whatever kind, must necessarily be abstract. Historical
resedirch itself begins by abstracting from all those innumerable
data influencing the problem at issue which are not mentioned
in existing historical documents ; and when it applies the
results obtained by the historical method to modern times,
or when it tests them — a3 it must almost always do — ^by
contemporary thought, it also abstracts from all the material
and spiritual changes of the intervening time — a, process which
may be permissible, but which may lead to serious error. If
this school were consistent, therefore, it should refrain from all
conclusions and from aU thought beyond the purely mechanical
recording of facts. Fortunately, it does not pursue its thesis
to its logical conclusion, but, on the contrary, has enriched
political economy by much extremely valuable research, which
will always retain its place among the treasures of the science,
even though it does not, and cannot, constitute the whole if it ;
and even though — ^Hke theoretical research — ^it cannot claim
more than approximate validity.

especially the eddies produced by the movement of the body. Another, and
older, example is Newton’s discovery of the speed of light through the atmos-
phere — ^which differed from the actual result by about one-third, because the
heating of the air under pressure had not been taken into account. Even
Newton’s famous Law of Gravitation at first gave an entirely incorrect result
when he tried to verify it, because one element m the calculation — the length
of the earth’s radius — ^was only imperfectly known.

PAKT I

THE THEORY OF VALUE

Bibliography. — Tlie tiiree works wMcli, appearing almost
simultaneously but quite independently, put forward for tbe
first time tbe main features of tbe modern theory of valu'^ are
Carl Monger’s Grundsatze der V olhswirUchaftslehre^ (published
after his death in a new and enlarged edition), Stanley Jevons’
Theory of Political Ecommyy and Leon Walras’ EUrnents
d^economie politique pure (both of which appeared in several
editions). The simplest, and perhaps fullest, presentation of
the theory, from Monger’s point of view, and without the use
of mathematical symbols, is given by Bohm-Bawerk in his
famous essay Grundzuge der Theorie des uArtschaftlichen
Guterwerts'^ {Conrads Jahrhucher^ voL xiii (1886)). An
adaptation of this, in which some portions of interest have
been omitted, is to be found in the same author’s Positive
Theorie des Kapitals, Among the many works in which the
theory was subsequently developed may be mentioned Marshall’s
Principles of Economics^ published in many editions ;
Wicksteed, The Common Sense of Political Economy ; Pierson,
Principles of Economics ; Pareto, Cours d^ economic

politique and Manuel d' economic politique (1909) ; my own
work, Vber Werty Kapital und Rente^; and, in Swedish, Johan
Leffler’s essays in Ekonomiska SamkdUslifvet, vol. i, pp. 4-37
and 48-80. Although supplemented and corrected by the
modern theories of value, the writings of the classical economists
on value and price have by no means lost their importance.
The well-known works of Adam Smith, Ricardo, and John
Stuart Mill still provide, in this field, a number of instructive
investigations and observations. A kind of reaction in the
direction of the earlier point of view, though more apparent
than real, is to be seen in G. Cassel’s Theoretische Sozialokonomie
(1918, 4th ed., 1927), also published in EngKsh (1923 and
1932).

^ [These works are reprinted in the Series of Scarce Tracts, pubbshed by the

London School of Economics.]

13

14 IJICTUEES ON POLITICAL ECONOMY

In this part we have first to examiiie the qnaKtative aspect
of human needs and the differing significance which we attach
to the available means, material, or otherwise, of satisfying those
needs. In modem communities this significance finds its most
striking and objective expression in the eocchange value or price
of the various objects, goods or personal services.

The theory of value and price has an importance which
is not limited to systems where there is highly developed division
of labour, with money and credit and more or less free competition.
Even in a self-contained economy (e.g. in the administration
of national or communal finance), indeed in every individual
productive enterprise or consumption unit, valuation constantly
takes place. And we find exchange, too, when that is understood
in the wider sense of the term, i.e. a choice between the various
uses of the same means of production or finished commodity ;
or between various means of achieving the same end. This
would stni be true if free competition ceased to exist, and gave
way to some form of collectivism. Hence the theory of value is
of fundamental and universal importance in economics.

Modem investigations in the theory of value have led to the
setting up of a principle — or rather to the generalization and
establishment of a principle already known and applied — called
the marginal principle, whose application extends far beyond the
actual province of the exchange of goods into the fields of
production, distribution, and capital. In other words, it governs
every part of political economy.

This so-called marginal principle is, in reality, only an
adaptation of the fundamental idea from which higher mathematics
and mathematical physics have developed ; namely, the idea of
regarding given magnitudes as variable (as a rule continuously
variable) quantities, and of regarding their rates of change as
new quantities (the Newtonian fluxions, the differential co-efficients
of Leibniz). It was, therefore, very natural that the refined
terminology and symbols of the infinitesimal calculus should be
applied to the modem theory of value. Yet, in the nature of
things, it is only the fundamentals of the calculus that can be
used, so that no more of it need be known than is taught in
schools.

There is ample reason, therefore, for inserting at this stage
in our exposition a thorough examination of the theory of value,

THEOKY OF VALUE 15

tkougli only in general outline and from a theoretical point* of
view. The realistic study of value or prices presupposes, ip the
first place, a knowledge of the theory of money and credit, the
treatment of which is postponed to the second volume ; and,
in the second place, an investigation into trade and marketing —
which belongs to a special division of economics.

For reasons of space we must omit many of the details
and abstruse borderline cases, in which the theory of value
abounds, and refer the reader to other more exhaustive accounts,
especially to Bohm-Bawerk’s essay in Conrad's Jahrbueher,
mentioned in the bibliography, and to the works of Marshall,
Wicksteed, and others.

1. Exchange Value and its Cateses, Earlier Explanations

The means of satisfying our needs we call utilities or
commodities — ^this last signifying utilities of a’ material kmd.
Immaterial utilities are called personal services, and these may
include services rendered to oneself ; for example, a walk, or
gymnastic exercises. Even rest and sleep are such personal
services and are just as important to the individual as those
performed by someone else. By goods we mean objects, many
identical units of which are available and which are the object
of trade.^

The word utility ’’ is related to useful, a term which has
many meanings : a thing may be useful in contrast to another
which is merely pleasant, i.e. which has a lesser and more
transitory use. More important, however, is the fact that most
things may have either beneficial or injurious ulterior effects ;
the latter may even predominate, but, being more remote, they
may be disregarded. Since, however, economic theory primarily
describes and explains human economic activity as it is, and
not as it should be, we must naturally include among utilities
those objects which, from a philosophic point of view, might
be considered harmful (e.g. many stimulants) so long as they
are objects of widespread production and consumption. The
Italian, Pareto, in his Cours d'economie politique, suggested that
instead of the word “utility” we should use “ ophelimite ”

^ [There follows, in the original, a paragraph which discusses questions of
termmology, which are of no interest to English readers.]

16 LECTUEES ON POLITICAL ECONOMY

(from the Greek — ^useful). But this seems unnecessary,

because there does not appear to have been any serious ambiguity
or misunderstanding in economic science concerning the various
meanings of the terms use or utility

Unfortunately, the same cannot be said of the closely related
concept of valm. Economists have disputed for over a century
— and are still disputing — about its correct meaning, or rather
about the relation between its different meanings. Happily, the
dispute has now lost most of its acerbity and seems on the point
of being abandoned. The definition of exchange value or price
offers no great difficulty and gives rise to no special ambiguity.
By exchange value we mean the ratio in which goods,
commodities or services are exchanged for other goods,
commodities or services, i.e. the quantity or number of units
of every other kmd of goods which may be exchanged
for a given quantity, or a given unit, of the first-mentioned
good. Thus, strictly speaking, a commodity has as many
exchange values as there are other goods, commodities, and
services for which it can be exchanged ; in this way, the
conception becomes indefinite. If, however, in exchange for
a imit of one commod one obtains, or must be satisfied
with, a smaller amount of all other goods, then we can reasonably
say that the exchange value of the first-named commodity has
fallen. We are accustomed in practice to use this expression
as soon as a rise or fall has occurred in the exchange value of
a commodity in relation to the majority of other more important
commodities, even if its exchange value in relation to one or
more less important commodities has moved in an opposite
direction.

The word price is sometimes used with exactly the same
meaning as exchxinge value ; but most commonly the price of
a good (and often its exchange value too) is supposed to be
measured in the general standard of values or prices for all
goods, which is called money Prom the various values
of goods in terms of money, their money prices — or, if we so
prefer, their money values— we can directly deduce, by division,
their relative exchange values. The problem of the theory of
value is to explain why one commodity has, either permanently
or temporarily, one price and another commodity (or service)
quite a different one.

THEORY OF VALX3E

17

At first sight it might appear that this valuation must
be due to differences of utility — so that exchange value and
usefulness would be one and the same thing — or at least
proportional to each other. And, in fact, it frequently is the
case that exchange value stands in a more or less direct relation
to usefulness. This is always true wherever two utilities can
replace one another and where both, even though more or less
effectively, can satisfy the same need. If, for example, we look
at our commonest fuels : beech, birch, pine wood, etc., it might
be argued that their varying prices or exchange values in the
market depend almost exclusively on their fuel value — on the
amount of heat obtainable from a given volume or weight of
each. Conditions are somewhat different with coal. In comparison
with an equal weight of wood, coal has great thermal efficiency,
but the various inconveniences and discomforts coimected with
the use of coal as fuel for a long time hindered its use for that
purpose, so that it had little exchange value. And its exchange
value is still low as compared with wood. The same is probably
true of lignite, peat, etc. Conditions similar to those prevailing
in regard to the above-mentioned three kinds of wood also
prevail between the various animal foodstuffs, such as pork,
beef, mutton, veal ; between the vegetable foodstuffs, such as
wheat, rye, oats, and potatoes, and to some extent also between
textiles — ^silk, wool, linen, and cotton, etc. But, as these examples
show, the relation between usefulness and exchange value is
not, even imder this assumption, quite evident and clear. In
many cases it does not appear to exist at all. Where, on the
other hand, two commodities cannot replace each other in
consumption, but either wholly or in part satisfy different needs,
it becomes a question whether their relative utilities can be
measured or compared by any common standard. Experience
also proves that the prices oJE two commodities often vary in
quite different degrees (and their relative exchange values thus
change) without there being any corresponding change in their
physical properties.

At the very beginning of the history of economic science,
attention was directed to this distinction.^ One of the best-known
passages in Adam Smith is that in which he explains that the

1 Indeed, much earlier, Aristotle brought out this very difference between
Krrjais (acquisition) and (usefulness).

18 IJICTDEES ON POLITICAL ECONOMY

word “ value two meanings, so that at one time it expresses
tlie usefulness of an object (or wbat lie calls its value in wse),
and at another its purchasing power over other utilities (i,e. its
exchange value). Adam Smith also pointed out that those things
whidi have the greatest value in use often have little or no
exchange value — ^for example, water ; and, on the other hand,
the things which have the greatest exchange value frequently
have little or no value in use, e.g. diamonds. But he stopped
at this point. He speaks afterwards only of exchange value
and never returns to the concept of value in use. And at this
point science stood stiQ, one may say, for almost a hundred
years without it being noticed that Adam Smith’s statement
was really a striking paradox and involved a problem which
necessarily demanded a solution. There were plenty of
commentaries and disquisitions on this statement in the
subsequent literature of political economy, but practically no
criticism, no examination of its obvious contradiction. . In what
follows, we shall endeavour to make such an examination.
But, before domg so, we must say something of the consequences
which this uncritical reception of Adam Smith’s statement
occasioned to political economy.

Since, as was assumed, utilities and exchange values did
not always coincide, but frequently diverged, exchange value
must either depend upon something entirely different from
utility, or upon utility and something else as well. The latter
explanation was generally accepted (though the Socialists, with
Karl Marx at their head, advocated the former). The result
was the concept of relative scarcity : in order to have exchange
value an object must, it was said, necessarily be useful, but, in
addition, it must exist in limited guaniities. If the supply is
unlimited in proportion to the need for it (air, water, and the
so-called /ree goods in general — ^in contradistinction to economic
goods, which do not exist in unlimited quantities and with which
we are, for that reason, economical), then the exchange value
falls, in spite of the great utility, to zero. On the other hand,
^eat scarcity can impart a high exchange value to objects of
little usefulness (though some usefulness must always be present),
e.g. rare stamps, animals, plants, precious stones, etc. With
a slight modification, this point of view developed into the
well-known proposition that if utility creates and regulates the

THEORY OF VALUE

19

detmnd for a tMng, its scarcity or the difficulty of producing it
regulates and controls its sujpjdy. Its price is, therefore,
determined, as we are accustomed to say, by the relation between
demand and supply. With a given supply, a large demand
leads to higher prices, and a small demand to lower prices.
And mce versa^ if the demand is fixed and the supply varies.
If utility, and with it demand, fails to zero, or iE it becomes
negative (so that people wish to get rid of the commodity),
then, of course, the price or exchange value will also be zero
or negative — ^people will pay to get rid of it (e.g. rubbish, slag,
and formerly even sawdust, etc.). Yet the same can also happen,
it was said, to useful objects if the supply becomes superabundant
— e.g. water in floods or cloudbursts, air when it comes in too
large quantities or too rapidly. Dwelling-houses, after all, are
principally designed to keep out an excess of air and water.
Again, if a relatively large demand encounters a small supply,
the exchange value may become very great, as, for example,
in the case of the demand for gold and jewels, which, even
ignoring the use of gold as a medium of exchange, are not
without use — even if only of a limited kind. They are, therefore,
eagerly sought for, but they can only be procured in small
amounts.

All this is, doubtless, in the main perfectly correct and
even obvious. But it is not the purpose of science to describe
the obvious in elaborate terms. If we examine the matter
a little more closely, the principle of the determination of value
by supply and demand does not, in reality, throw much light
on the real nature of the phenomena under discussion. It is
obvious, for example, that only so-calied effective demand
influences prices. The demand of persons who are not in
a position to pay the price asked for any particular commodity
evidently has not the slightest influence on price, however great
that demand may be. It may be compared to the longing
glances of the numerous, though impecunious, persons who
gaze at the precious objects in a jeweller’s shop window. But
the efl^ective demand — ^in other words, the quantity of the
goods that can be bought at the prevailing price — ^is, on the
average, neither great nor small in relation to the supply, but
is in fact exactly the same. Indeed, it is only on this condition
that the market can be in a state of equilibrium. If the demand

20

LECTUEES ON POLITICAL ECONOMY

is greater than the supply the price will rise ; if it is less the
price will fall — ^but it cannot continue to rise or fall for ever.
Since, therefore, supply and demand are equal where there is
economic equilibrium and a stable price, whether that price
be high or low, we must further ask : l^y does the demand
for and the supply of this particular commodity achieve
equilibrium at one particular price, and that of another commodity
at a totally difierent price ? The classical analysis of exchange
values gives no direct answer to this question, though this
drawback was felt by the classical economists themselves.

It may be pointed out that, in Adam Smith, the expression
effective demand has a somewhat different meaning. It
means the demand of those persons who are willing to pay the
“ natural price i.e. the costs of production and transport ; if
supply in the particular case were accidentally greater or less than
this demand, then the price would fall below or rise above the
natural price

P. J. Neu^nn, m his essay on ‘‘Value’’ in Schonberg’s
Handbuch, entirely rejects the concept of supply and demand
(offer and demand) whenever these are regarded as merely
quantities.^ That, in his view, is extremely one-sided. On the
contrary, in his view, supply and demand represent a whole
complex of qualities : extensity, intensity, purchasing power on
the part of those who demand, etc. ; for which reason it is absurd
to say that demand is as great as, greater or less than, offer or
supply. The obvious reply to all this is that the circumstances
enumerated by Neumann doubtless affect the magmtude both of
supply and of demand, and the total result must be that, when a
certain price is quoted in the market, a certain definite quantity
of goods of this kind will be offered and an equally defimte quantity

mn be demanded. For my part, I cannot see the one-sidedness
01 such a view.

Without entirely abandoning the formuk of supply and
demand to which they always resorted in case of need, attempts
were made by the classical school to provide a more definite
explanation of the exchange value of at least one group of
coi^odities (m practice the most important), i.e. those which,
as It was usual to say, could be produced in unlimited quantities.

THEORY OF VALUE 21

The explanation related to their cost of ^production or eventually,
according to a subsequent variation of terminology, to their
cost of reproduction. If a commodity is not, generally speaking,
an object of production in the ordinary sense (as, for example,
certain natural products), or cannot be produced or reproduced
(pictures by old masters), or if, finally, its manufacture is the
result of a natural or legal monopoly, then we must still content
ourselves with the thesis that the price is determined by supply
and demand. For the majority of goods, on the other hand,
which can in practice be reproduced in unlimited quantities
under free competition, costs of production would, as has been
said, determine the average or ‘"naturaU" price, about which
the market price always oscillates.

It is quite evident that, imder free competition, the price
of a commodity cannot be either above or below its cost of
production if this includes everything required for bringing the
commodity to market, including a “ reasonable (i.e. customary)
compensation to the last seller for his labour and trouble.
If it were otherwise, the commodity would either not be
manufactured, or it would be manufactured in such large
quantities that the price would necessarily fall owing to the
increase in supply. But if this is to be a valid explanation of
reciprocal (relative) exchange values, then the costs of production
must evidently be something definite, something arising from
independent (absolute) causes ; they must not be dependent
on the exchange values themselves. Herein lies the weakness
of the classical theory of value. If we analyse more closely the
conception of costs of production, we shall find that the latter
resolve themselves into a reward or compensation for the use
of the various factors of production, usually divided into the
three main categories of land, labour, and capital. If, for example,
the manufacture of two quantities, a and 6, of two diSerent
goods requires the same amount of the same kind of labour,
the employment of the same quantity of land of the same
quality and the same quantity of capital for the same period
of time, then we can say without fear of contradiction that
both quantities of goods will be sold in the market at the same
price. That is, after all, nothing more than saying that all
labour of the same kind, all land of the same quality, and all
capital employed for the same period of time will receive the

22

LECTURES ON POLITICAL ECONOMY

same reward, wMch is a natural and necessary consequence of
free competition. If, on the other hand, as is nearly always
the case, the production of these commodities requires land,
labour, and capital in different, proportionSj e.g. more land, but
less labour and capital, for a than b, then some means
must be found for reducing the quantities of these various factors
of production employed to a common measure, though, of course,
no direct means of doing this is available. In order to e:spress
them in common units, we have to refer to the remuneration
they demand, i.e, the relative magnitude of wages, rent, and
interest. These, however, are not given, and the determination
of them constitutes a problem of the same kind as our original
problem, and one which can only be solved in connection with it.

The method adopted by economists of the classical school
(particularly Ricardo) to escape from this dilemma shows
considerable ingenuity; but as has been seen already from
our consideration of the connection between the market price
and the costs of production of a commodity, and as we shall
show in further detail later, the attempt was foredoomed to
failure. In the iBxst place, they attempted to simplify the
problem as much as possible. The various kinds of labour,
such as skilled and xmskilled, might, they thought, be reduced
to a common standard in so far as labour of a higher quality
was regarded as representing an extra number of working days,
corresponding to the higher wages paid for it, and to the time
which the workman had previously spent on his technical
education. As regards capital, they found its chief r61e in
production to lie in advancing wages or the necessities of life to
labourers and providing necessary tools and raw materials.
They assumed in consequence that capital (or the capitalists)
iu an branches of production would receive approximately
the same share or percentage of the exchange value of the
product (profits of capital). Ricardo expressly admitted that
this rule was subject to important exceptions in consequence
of the mequal proportions of fixed and circulating capital in
the various branches of production. Finally, they thought that
land could be disregarded and that rent could therefore be
excluded from costs of production. They only regarded labour
and capital employed at the margin of production as contributing
to costs— either on marginal land, the least fertile (which is

THEOEY OF VALUE

23

superabundant and, therefore, pays no rent) or, in more intensive
cultivation, on land which is already employed — ^where an
addition to output can pay no extra rent for similar reasons.
In this way, the factors of production governing exchange
value were reduced practically to one only — ^labour. According
to Jlicardo, the exchange values of various goods should stand
in more or less direct relation to the quantities of labour
required to produce them under the most unfavourable
conditions which are necessary for their production, i.e. on the
margin of production. So great was the satisfaction felt with
this result, which is formally so brilliant, that J. S. Mill in the
introduction to his theory of value declared the classical theory
of value to be "" complete ”, so that there remained nothing
for him, or for subsequent writers, to add.

Eioardo makes another simplifying assumption, which must
be borne in mind m reading his works, if we are not to misunder-
stand them. He assumes that gdid^ the measure of value and
prices, is always produced with the same labour costs, and also
that profits on capital employed in the production of gold constitute
the same percentage of wages or of the total product as in any
other branch. From this he is led to the conclusion that the
amount of labour employed in the production of a certain unit of
goods directly expresses the number of ounces or grammes of gold
for which this unit of goods is habitually exchanged in the market ;
in other words its 'price measured in gold. On this assumption,
on the other hand, the general level of wages can never have the
least efiect on prices, as in that case they would also affect the
price of gold (in money, i.e. reckoned in gold), which is an obvious
contradiction. A rise in wages (money wages) can, moreover,
according to Kicardo, take place only in combination with a
corresponding fall in the profits of capital, where commodity
prices remain unchanged ; a change in commodity pnces, again,
necessarily presupposes that the amount of labour employed in
their production has — owing to new inventions or to increased
difficulties in production — become greater or less than
previously.

By these various simplifying assumptions Eicardo greatly
facilitated his analysis. In his work, the structure of economic
theory appears, for the first time, as a coherent, logical system.
But his conclusions thereby frequently assume an abstract and
even unreal character. In this respect, he compares unfavourably
with Adam Smith.

24 LECTUEES ON POLITICAL ECONOMY

Even if we admit all these generalizations and simplifications
for what they are worth, we are still faced with the fundamental
error of the classical theory of value. Their margin of production
is not a fixed limit, given a priori, but is variable and itself
depends, among other things, upon the actual exchange
value of the goods in question and, to that extent, upon what
it has to explain.

Thus, for example, there are certain manufactured goods
(especially articles of clay) for which the raw materials exist
already mixed in nature in practically unlimited quantities, so
that, for them, there is no margin of production : they can be
produced with unchanged labour costs (per unit of goods) in any
desired quantity. In the case of other commodities, on the
other hand — ^particularly the means of subsistence — ^in any given
state of technique, increased labour costs per unit are necessary
if they are to be produced in larger quantities than before.
If, therefore, any economic unit must itself provide for the
production of these two kinds of goods, their relative exchange
value or price will clearly depend, to a high degree, on the
relative magnitude of the demands for them ; for the extension
of the margin of production and the costs of production at that
margin for the latter commodity are only thereby determined.

Let us take another example. Suppose that an economic unit
(a district or a whole country) is compelled by natural circum-
stances to restrict its production to two staple articles only, say
com and Imen, the prices of which we will suppose, for the moment,
to be determined by the world market. If the price of linen goods
is relatively high, the community will devote itself principally
to their manufacture and will crdtivate corn only in proportion
to its domestic needs ; if, on the other hand, the price of corn is
relatively high, then it will expand its production of corn and
restrict its manufacture of linen to the minimum. Since, however,
the production of linen requires little land in proportion to the
labour employed, it is clear that, in the former case, when linen
is the chief manufacture, the demand for land will be small, and
agriculture will be restricted to the best land or will become less
intensive. In both cases the result will be that the labour employed
in the production of raw materials will become, even on the
margm of production, inconsiderable. And, since this labour in
the case of corn constitutes the whole, and in the case of linen
only a minor part, of the necessary labour, the portion of labour

THEOEY OF VALUE

25

employed per unit of linen will be great m relation to that employed
in tbe production of a unit of corn. On tbe otlier band, if tbe
production of corn, owing to changed price conditions, becomes
predominant, the production of the raw material must be extended
to inferior land, or else the cultivation of the better land must
become more intensive. Whichever happens, the result will be
that the amount of labour which is employed on the inferior land
(or, in general, on the margin of production) in the production of
the raw material will be very great. From this it will follow
further that the total labour employed under the most unfavour-
able circumstances in the production of one unit of corn will be
relatively great in relation to the labour employed in the production
of one unit of linen. As illustrations we may mention the economic
conditions in Northern Russia, Ireland, and, to some extent,
certain Swedish provinces, at the time when the increasing
cheapness of cotton goods began to oust the native linen products
of those countries.

A third, and very important, example is the exchange value or
purchasing power of gold itself in terms of goods, which — as even
Adam Smith realized, though Ricardo purposely ignored it — ^is by
no means constant, but depends on the labour costs in the mines
on the margin of production. Naturally, however, this margin
is itself variable. It expands when commodity prices are low and
the purchasing power of gold is high, but it shrinks in the contrary
case ; so that production is restricted to the richer mines or river
beds, and the maximum labour employed in the production of a
given quantity of gold becomes less.

In such cases, Ricardo’s thesis that the exchange value
of the product is proportionate to the quantity of labour required
for its production at the margin is verified — ^if in each case, as we
have done, we do not take into consideration the varying
proportions of capital employed. Yet obviously, under such
circumstances, it is not the costs of production which govern
the exchange values. That, indeed, would be impossible if,
as is assumed in the above example, the latter are fixed and
determined beforehand by the world market. On the contrary,
it is the exchange value of the goods which governs their costs
of production — i.e. which determines how much labour shall be
employed in the production of one unit of com and in one unit
of linen goods. Again, if we look at the matter more generally
and observe either an isolated economic unit or the whole of
the world’s production and exchange, then it is clear that costs

26 LECTUEES ON POLITICAL ECONOMY

of production and exchange values cannot stand in the simple
relation of cause and effect which Eicardo supposed. As we
s hall ^ later, they are muimlly conditioned like the various
elemente in a single economic system in equilibrium. But, in
that case, it is ^Iso clear that reference to costs of production,
even under the simplest imaginable assumptions, is impossible
as a theoretical explanation of the exchange value of goods,
however useful it may often be as a practical rule.

No doubt, the classical economists failed to realize this
because, in the case of one of the most important groups of
commodities, the means of subsistence, they regarded demand,
or consumption (and therefore also the extension of the margin
of production), as given by the size of the population. Statistics
have not confirmed this : largely owing to indirect methods
of use, the demand for and consumption of com and other
foodstuffs is almost as elastic and variable as that of other goods.

There is this further point. It happens in many cases, even
where a commodity is manufactured under competitive conditions,
that its costs of production cannot he separated or imputed
because its production proceeds simultaneously and in
combmation with that of other goods, e.g. where one commodity
is a by-product in the manufacture of another. Such cases, which
have been given by Marshall the technical name “ joint supply ”,
are mentioned also by Mill in his chapter, Some peculiar cases
of value,” ^ but, as the chapter heading indicates. Mill regarded
them as exceptions to the rule. In reality (as Jevons remarked)
they occupy a large, perhaps the largest, part of the field of
production. We shall return to this subject m greater detail,
but it may be pointed out here that all branches of agriculture
faU within the category of joint supply : the cultivation of cereals
and livestock, no less than that of textile materials and other
commercial crops, are mutually determined in any well-ordered
system of agriculture. Here the only question which arises is
whether the total selling value of the products will cover the
total costs of production, for the separate costs cannot be
imputed. When, for example, before the introduction of corn
duties in Sweden, some agriculturists maintamed that the
growing of rye at the low prices prevailing did not pay ”,
they nevertheless continued to grow it and proved by so doing
^ [Principles, book iu, chap, xvi.]

THEORY OF VALUE

27

that this crop constituted a necessary element in an agricultural
system which must have paid as a whole, or else it would have
been abandoned.

Here also, it would be possible, by an artifice resembling that
of Ricardo for the elimination of rent from the costs of production,
to impute the costs of various goods by supposing that one or
other of them entered in varying degrees into the total output —
which is in fact in full correspondence with actual conditions.
Thus, for example, a breeder of sheep produces, at one and the
same time, wool and mutton, but he can, as required, specialize
on one breed of sheep or another, the wool-producing or the
mutton-producing, and in that way obtain either more meat and
less wool or vice versa. The possibility of transporting fresh meat
in refrigerating chambers from Australia or the Argentine to
Europe in fact compelled European sheep farmers to abandon
the merino breed, with its fine wool, in favour of breeds yielding
more meat. This, in its turn, gave rise to a crisis in the European
clothing industry towards the end of the nineteenth century.

In the same way, in the manufacture of coal gas, coke is
obtained, if desired, as a by-product. But here, too, the pro-
portion between the two products is neither given nor determinate,
for some coal yields more gas and less coke, and vice versa. If
coking is the principal objective, as at iron works, more attention
will be paid to the latter kind of coal, and vice versa if the produc-
tion of gas is the more important. In this way, we obtain a kind
of margin of production in which an increased production of one
of the commodities corresponds to a definite increase in the costs
of production. But even here it will appear that the costs of
production are by no means pre-determined ; they may vary in
a high degree with the variations in the relative prices of the
goods. In other words, the relation between costs of production
and exchange values is, in this case also, not one of cause and
efiect, but of interdependence.

In reality, the classical theory of value did not give general
satisfaction. The celebrated Proudhon included, though on
somewhat confused grounds, the theory of value among his
Contradictions iconcmiques^ and Bastiat, his opponent, introduces
the chapter on value in his work. Harmonies economiques^ with
the significant words Dissertation ennui : dissertation sur la
valeur, ennui sur ennui ’ A theory which one has fully mastered
does not, however abstra6t, normally give rise to ennui. The
modifications which these men and the schools to which they

28 LECTUEES ON POLITICAL ECONOMY

belonged effected in tbe tbeory of value were, bowever, by no
means improvements. On the contrary, both of them expanded
the classical attempts at generalization to exaggerated paradox.
In the hands of the Socialists (especially Eodbertus, and Marx
still more so) the theory of value became a terrible weapon
against the existing order. It almost rendered aU other criticism
of society superfluous. Labour was conceived by them — ^Ricardo
never meant or said any such thing — ^to be the sole creator of
value — ^in other words, the source of value ; and thus aU other
factors of production existing in private hands were to be
* regarded as parasites on production, and their rewards a robbery
at the expense of labour, which is alone entitled to remuneration.
The fallacy of this reasoning will be made clear in what follows.
The harmony economists, Carey, Bastiat, and their numerous
disciples in different countries, believed, on the contrary, that
they had found in the principle of labour as the only creator
of wealth a highly effective weapon for the defence of the existing
order of society. They attempted, indeed, to reduce all the
shares in the product, even including the rent of land, to wages
of labour (i.e. wages for the labour which had been employed
on the land or m production in days gone by).

The absurdity of such arguments is obvious and has perhaps
contributed more than anjrthing else to the charge of dishonesty
and subservience to the interests of the powers that be which
has been levelled against scientific, or quasi-scientt&c, economics.
In Karl Marx's theory of value the Socialists believed that they
possessed a theoretical foundation as good as that which was
offered by the harmony economists, and both sides considered
that they were fighting, with as much or as little justification,
under the banner of classicism.

The establishment of a new and better-founded theory of
exchange value was, therefore, not only of abstract theoretical
importance, but also of eminent practical and social interest,
and the three men who almost simultaneously and independently
succeeded in doing so — ^the Austrian, Carl Menger, the
Englishman, Stanley Jevons, and the Frenchman, Leon Walras ^

^ To some extent, the German, H. H. Gossen, whose work appeared in 1854

but was entirely neglected during his life-time, ought to be reckoned a
predecessor of all three. Yet neither Gossen — ^nor, for that matter, Menger —
went so far as to establish the proportionality between the marginal utility
of mfferent goods, which, as we shall see, constitutes the law of free exchange
and which is put forward in essentially the same form by Jerons and Walras.

THEORY OF VALUE 29

— ^thereby payed tbe way, more than is usually supposed, for
mutual understanding even in the social field.

2. The Concept of Marginal Utility

A, presentation of the modern theory of value may, as has
already been indicated, conveniently proceed from a revision
and analysis of Adam Smith’s thesis relating to the divergence
between value in use and value in exchange — ^which he
exemplified by water and diamonds (cf. p.* 18). Literally
interpreted, this thesis appears to be either meaningless or
a contradiction in terms. In the first place, which value in
use has he in view ? Evidently it cannot be the utility of water
or diamonds in their totality, for even if it were at all possible
to exchange all the water for all the diamonds in the world
it would soon become clear that the former had an infinitely
greater exchange value than the latter ; of course, the comparison
must relate to manageable quantities, e.g. a litre of water or
a diamond weighing one gramme. But, even in such a case, as
Mill remarks, the value in exchange cannot possibly be greater
than the value in use (though it may be less, according to Mill),
for we should otherwise be confronted by the absurdity that
a person would dispose of a more useful for a less useful
commodity. In other words, the value in use, according to
Mill, constitutes the upper limit of value in exchange. But on
further consideration it appears that the value in exchange
cannot be lower than the value in use either, for exchange
presupposes two exchanging parties, and while no one will buy
a commodity which has a value in exchange higher than its value
in use, no one will sell a commodity whose exchange value is
lower. We thus seem to arrive at the remarkable result that
value in use is, at one and the same time, the upper and the
lower limit of exchange value ; or, in other words, is its exact
equivalent. This, however, is contrary to experience ; neither
is it easy to understand how, under such circumstances, any
exchanges whatever could be effected. The obvious explanation
is the well-known fact that the same thing may possess different
degrees of utility for different persons, so that the relative values
in use can, at the same moment, be greater or less than the
relative exchange values for one or other of the exchanging parties

30 LEOTORES ON POnTICAL ECONOMY

fe^p&iivdy. If we follow up tMs train of thonglitj we stall
easily see ttat a thing may have quite different degrees of
utility for one and the same person under different conditions.
The most important circumstance in this connection is evidently,
at least in a primitive economy, the quantity of the commodity
in one’s possession — or of other commodities which can, to
a greater or lesser degree, replace it. In a more advanced
economy, the dete rmining condition will be the possession, or
accessibility, of a certain quantity of the medium of excJmnge —
that is, of the commodity in exchange for which, as experience
shows, other commodities can be obtained. But what sets the
standard in both cases is, in the last resort, the quantities of the
various commodities which the person in question is in a position
to consume in a given unit of time.

Value in use is,' therefore, by its very nature, something
variable. Value in exchange, on the contrary, is always, or
always tends to be, constant and invariable for each commodity
throughout the market. The question then becomes : which of
these possible, or conceivable, degrees of value in use determines
(or, to express ourselves more cautiously, is related to) the actual
exchange value of the commodity ? The answer must evidently
be : the degree of utility which it possesses for the exchanging
parties at the moment the exchange is effected, whether that
utility arises from then* present or future needs. That, however,
is evidently hardly ever the maximum utility which the
commodity in question might, under certain circumstances,
possess, nor even the average utility which such a commodity
usually possesses, but rather the minimum utility which the
commodity, or one unit thereof, under the given circumstances,
mill jiossess or may conceivably possess. This degree of utility
is what is called the marginal (or final) utility of a commodity,
and corresponds, therefore, to the least important of the needs
satisfied by the acquisition of that commodity — ^and that is the
same as the most important of the needs which are not satisfied
if the commodity is not acquired, or is acquired in lesser quantities.
As regards the commodities given in exchange, their marginal
utility will correspond to the least pressing of the needs which
w”!!! be satisfied if they are not offered in exchange, though as
regards very small quantities this cannot be distinguished from
the least pressing of the needs which, after a completed exchange.

THEOEY OF VALUE

31

remain unsatisfied. Tlie result is tliat, after an excliange lias
been effected, tbe marginal utilities of botb commodities /or each
of the exchanging parties stand in tbe same relation as tbeir
common excliange value. If this were not the case then, as we
stall stow later, one of tbe parties would desire to excliange
furtber and, by offering a somewhat more advantageous price,
would induce the other party to consent.

An easily comprehensible example of the variability of value
in use is the well-known one given by Bohm-Bawerk (originally
given in almost the same form by Menger). A colonist hving
alone in the virgin forest by agriculture has just harvested five
sacks of com (excluding that set aside for seed) which constitute
his entire supply of foodstuffs until the next harvest. If he
disposes of this stock in accordance with his previous consumption,
every sack will have a different use and will therefore be of different
importance to him, although physically they are all identical.
The first sack is absolutely necessary for the maintenance of
life and is therefore as valuable to him as life itself. The second
sack is still of the greatest importance to him, because with it he
can eat his fill and preserve his health and bodily strength. The
third sack he will no longer consume directly but will use to keep
fowl and thus procure a necessary change in an otherwise purely
cereal diet. The fourth sack he may use for making spirits. For
the fifth sack he can find no better use in his simple mode of life
than to employ it for his own amusement in providing for a few
parrots. If, by some accident, he should lose one of his sacks of
grain, then it is clear that, under such circumstances, it would be
the fifth sack which he would sacrifice, i.e. the least important
from the point of view of the satisfaction of his needs. If he lost
another it would be the one used in the making of spirit, but not
one of those which was required for his real sustenance ; and so on.
Strictly speaking, there also exists a certain gradation within the
sphere of each of these utihties : it is quite possible that he would
renounce a little of the satisfaction of the more important needs
before he entirely abandoned those which, regarded as a whole,
rank lower in the scale of utility. But we shall soon return to
this point.

By means of this simple conception, the theory of value has
obtained the clearness and coherence which it formerly lacked.
The dualism inherent in the traditional conception of exchange
value as requiring two quahties, utility and scarcity — ^though

32 LECTURES ON POLITICAL ECONOMY

it was never clear in what relation they stood to each other —
now disappears, in so far as marginal utility actually represents
a sy^uTiesis of utility and scarcity. Marginal utility becomes the
degree of utility at which the consumption of a commodity must
cease precisely because of its scarcity. The term scarcity {rarete)
was used by Walras as exactly equivalent to marginal utility
(his father, Auguste Walras, had earlier employed the same
word) ; for he regarded a commodity as scarce only when it
exists in insufficient quantities in relation to the need or demand
for it — ^so that the degree of scarcity is indicated by the marginal
utility. This is, of course, a matter of taste ; but Walras’
terminology is somewhat forced and has not found general
support.

Thus, if a relatively scarce commodity (e.g. a choice wine)
has a high exchange value, it is due to the fact that consumption
must cease at a point where the least important of the needs
satisfied and the most important of the unsatisfied needs or
degrees of need (of choice wine as refreshment or as a stimulant)
are still of great significance ; whilst common commodities, such
as bread, are usually consumed in such large quantities that the
need which one more unit per consumption period could satisfy
is of relatively little significance, or of none at all (as is usually
the case with the free goods, air, water, etc.). It is of no
importance, in this connection, that the category of needs which
bread satisfies (the maintenance of life) is, as a whole, much
more important than the category which is satisfied by wine,
namely, the need for refreshment and the satisfaction of more
refined appetites. The same conditions apply here — ^to use, once
again, a simile from Bohm-Bawerk — as in the case of two
mountain heights. One of them is, absolutely, much higher
than the other, but this does not prevent a climber at a given
moment from being situated much higher up on the lower
mountain than another climber on the higher mountain.

It was this relation which Adam Smith overlooked. The
value in use on which his gaze was fixed, and which in his view
might often stand in inverse relation to exchange value, was
evidently the maximum utihty which the commodities compared
(water and diamonds) could respectively attain under given
conditions. But the parties to the exchange have nothing at all
to do with this ; they are, of course, only concerned with the

THSOEY OF VALUE

33

actual or prospective utility whicli the commodities possess for
them at the moment of the exchange. Bearing this in mind,
one is almost tepapted to turn Adam Smith’s thesis upside
down and to say that those commodities which have a high
exchange value thereby prove themselves to possess great value
in use or high utility — ^i.e. high marginal utility. Yet such
a formulation would not be quite accurate, for the individual
differences among consumers, and especially their different
financial positions, here play an important role. To the rich
man, who can fully satisfy practically all his needs, all
commodities must have a very low marginal utility : if a rich
man spends hundreds of pounds on a single diamond, that does
not prove that it has a higher value in use for him than for
others. In most cases it only means that the commodities, the
consumption of which he forgoes in order to procure the diamonds,
possess for him little or no value in use. Indeed, as we shall
see later, we find, in arriving at the laws of price formation under
free competition, that the degrees of utility — ^the relative
marginal utilities — of the same thing to two different persons
are never compared, but only the marginal utilities of different
commodities to a single individual. If, however, property and
income were more equally divided, it would no doubt appear
that the scale of values in use for most persons would more
or less coincide — and this would produce the result that
diamonds and many things now highly esteemed would fall in
exchange value, and their production would decline — ^perhaps
suflicing merely for the provision of enough diamonds for glass
cutting and drilling. There was a striking example of this in
the world crisis of 1907, when the world-wide reduction in
profits led to a special crisis in the Dutch diamond industry.

A question which has, perhaps, already occurred to the
thoughtful reader and to which we will not postpone the answer,
is the following. It seems clear that marginal utility determines
exchange value so long as it is only a question of obtaining, or
disposing of, a small quantity of a certain commodity in exchange
for a similar small quantity of another ; and so far as one is
already provided with a sufficient, or nearly sufficient, quantity
of both. But actually, in a modern economic society, based on
division of labour, we obtain practically ail commodities, or at any
rate a large proportion of them, exclusively by exchange. Thus

U LECTURES ON POLITICAL ECONOMY

tkose commodities in fact satisfy aU our needs — even those of the
highest degrees of intensity. How then does it come about that
exchange value as a whole is only regulated with reference to the
last and least important of these degrees of need ?

This observation is fully justified. In actual fact, exchange
value is by nature just as variable as value in use or utility^ In
isolated exchange there exists, as we shall soon see, funda-
mentally no such thing as a uniform exchange value. The more
or less feed proportions in which, as we know by experience, goods
are exchanged for each other in the market, and which have given
rise to the name and concept of exchange value, are something
peculiar to the market as stick or to the influence of the market —
and not to individual exchanges independently of the market.
That something is free competition on the part of either or both
parties to the exchange. As Jevons expressed it, there is operating
in the market the law of indifference It is a matter of
indifference to buyer and seller alike with whom they do business
provided that they obtain the same goods or the same price, as the
case may be. For this reason there can be, roughly speaking, only
one price in the market, for a given commodity at any moment
of time.

Fundamentally, marginal utility and exchange value or price
will stand in the same reciprocal relation of dependence as that
which we have already found to exist between exchange value and
marginal costs of production. If the exchange values are given
beforehand, e g. as they are given in a small economic unit, by
the influence of the world market, then the marginal utilities will
be regulated by them ; for the various goods will be consumed up
to the point where, for each and every consumer, their respective
marginal utilities stand in the same relation to each other as the
exchange values or prices. If the exchange values are not given
in advance, but are determined by the market proper then
marginal utilities and prices will mutually determine each other
in a single system of eqmlibrium and they can be symbolically
or hypothetically expressed by a system of equations, in which the
goods available in the market, or for the period of consumption,
constitute the known quantities in the problem. But actually
even these quantities are not given ; goods are in most cases
constantly being produced and consumed and can, according to
circumstances, be brought to market or withdrawn from the
market in larger or smaller quantities. The final problem of
equilibrium, the problem of eguilihriy/m between production and
consumption by means of exchange, therefore includes among the

THEOEY OF VALUE

35

unknowns tke quantities produced and consumed and tke relative
exchange value of the goods, as w’ell as the proportional marginal
utilities for each particular individual. On the other hand, the
definitely known quantities are the means of production existing
at each particular moment : labour, land, and capital (and if the
process extends over a longer period, factors affecting the accumula-
tion of capital), as well as the individual dispositions of con-
sumers. The exchange value must then be fixed at a level such
that the forces on the two sides balance ; i.e. the desire to consume
(the utility or satisfaction of consuming) on the one hand, and the
difficulty of producing, the inconvenience or discomfort of manu-
facture (sometimes called negative utility or disutility), on the
other. That the marginal utility or disutility should be the
decisive element is quite in accordance with a number of other
apparently paradoxical phenomena of equilibrium (cf. the so-called
hydrostatic paradox) ; but, at the same time — ^though this is
unsatisfactory from the ethical and social points of view — it
shows the purely mechanical character of the economic phenomena
which occur imder conditions of free competition.

We shall now endeavour to explain in more detail the
complicated phenomenon of exchange equilibrium, following the
principle strictly pursued throughout this book (as in Walras’
work) of proceeding successively from the simple to the
complex.

3. Free Exchange and Market Valm

A, The Different uses of a Single Oomrmdity

In the market, we observe a double phenomenon : the
determination both of the magnitude of the volume of goods
exchanged, and of the ratio in which they are exchanged. If
there are only two commodities, this ratio is, as a rule, a direct
consequence of the quantities of the goods exchanged ; but not
if there are more than two. But for the present we shall
make the assumption that the ratio (or ratios) of exchange are
for some reason given and fixed, so that it is only a question
of determining the absolute quantities exchanged ; if there are
only two goods, their relative magnitude is thus already given.

The simplest conceivable form of exchange is that in which
one and the same person chooses between different uses of

$6

LEOTUKES ON POLITICAL ECONOMY

a single commodity. Let ns, for example, return to B5km-
Bawerk's colonist in the virgin forest and Ms stock of five sacks
of com (see p. 31). But now suppose that he had only two
uses to choose between : either direct consumption in the form
of bread or cereal food, or indirect consumption in the form of
meat wMch he obtains by using a part of Ms stock of com-for
poultry breeding. For the sake of simplicity, we shall ignore the
additional trouble and inconvenience wMch he incurs in following
the latter alternative. We may then conceive his operations as
a sort of exchange, in wMch the exchange value is determined
by technical circumstances : by sacrificing the direct consumption
of so many kilograms of com he can, if he wishes, obtain one
Idlogram of eggs or fowl. The only question is what quantities
of his original stocks will, economically speaking, be offered in
exchange.

If we were to think of the utility (or value in use) of each
article of consumption as a fixed quantity, we should arrive at
the absurd conclusion that he must convert either all or none
of his com into fowl or e^, according as the utility of the
latter is greater or less than the utility of the former. The case
is quite different if, in accordance with reality, we suppose the
utility of a unit of goods to be a variable quantity, wMch,
ceteris paribus, is reduced when the number of units available
for consumption increases. The colonist had no need at all for
the last sacks of com as food ; their utility for direct consumption
was thus zero — or even negative. But the addition to his cohort
and well-being resulting from the consumption of the first
portions of animal food per unit of time — e.g. an egg or a roast
cMcken a week — ^is very considerable. Thus, if he converts the
last sacks of com into poultry, he adds considerably to the
utility wMch would otherwise have been attainable. If he
sacrifices another sack for the same purpose, his gain on the
exchange will stiQ be considerable, though not as great as from
the first, because he might have derived a positive advantage
from using this sack for direct consumption, and also because
the desire for animal food is not so strong when it has already
been partially satisfied. The same is true in an even higher
degree of the third sack. The sacrifice of a part of this sack
for poultry breeding might possibly increase its utility, but for
the other part he would presumably prefer the direct use and

THEORY OF VALUE

37

would consider that he had lost on the exchange if he used it
for conversion into animal food. Economy demands a line of
demarcation between the portion of the original stock of corn
which is given up and that which is retained ; and this evidently
lies — at least if we assume that the quantities in question are
continuous variables — ^at the point where the last Miogram of
corn has the same or about the same utility, whether it is
consumed directly or converted into animal food. In other words,
the rmrginal utility, the utility of the last kilogram consumed
directly and of the last converted into animal food, must, in
economically-regulated consumption, be the same. Or, in other
words, if we assume that 5 Idlograms of com are required for
the production of 1 kilogram of chicken or eggs, then the utility
of the last kilogram of animal food would be five times as great
as the utility of the last kilogram of cereal food, so that the
marginal utility would be proportional to what we may here call
(though not altogether appropriately) the exchange value.

The position would naturally be exactly the same if, instead
of only two uses for the original stock of com, there had been
three, four, or more. However difierent the significance of the
various uses— to sustain life and health, to improve diet, to
provide enjoyment or trivial diversion — ^may be, one thing is
certain : that, of the portions used for each of these different
purposes, the last Idlogram will procure for its owner, at any rate
approximately, the same amount of satisfaction or utility.
Otherwise it woxdd be inexplicable why he did not, from the
begin nin g, either use that portion for a purpose which would
bring him greater advantage, or, if he had made a mistake
from lack of foresight, did not rearrange his plan of consumption
for the ensuing year accordingly. If, instead, we measure the
various methods of consumption by their own particular units —

1 kilogram of com, of meat or of eggs, 1 litre of spirit or one
parrot — ^then, obviously, their marginal utility will, in every
case, be proportional to their relative exchange values

This provides the answer to some of the objections which
were raised to the theory of marginal utihty when it was first
propounded, and which one still sometimes hears. To the
ordinary mind, the utilities or values in use of various goods
appear as something incapable of comparison, as incommensurate
quantities ; they were thus described by Ricardo and, after him.

38 LECTURES ON POLITICAL ECONOMY

by Karl Marx. To compare hypothetically the utility, or marginal
utility, of various com m odities, as the modem theory does, seems
a priori absurd ; and to try to measure utility exactly — ^to
maintain that the marginal utility of an object or of a class
of goods is so many times greater than that of another — is, at
first sight, as absurd as to say, with E. J. Neumann, that ‘‘-one
person is one and a half times as polite as another And yet,
as the above example shows, we all make such a comparison
at almost every moment of our life. Neither does the idea of
exact measurement really involve an absurdity ; if we c^n
generally say that a certain unit gives a utility equal to, or
somewhat large or smaller than, that of a different unit, then we
can also say the same of two, three, four, or more imits of the
one kind in comparison, with one or more units of the other.
And, in fact, we meant nothing else but this when we said, in
reference to corn and animal food, that the marginal utility of
the latter was about five times as great as that of the former.
It is tme that one assumes that each of the 5 kilograms of corn,
which are compared with 1 kilogram of poultry, has the same
utility. But this assumption can be made without any risk with
reference to small portions of a large stock, as indeed is often
done in corresponding cases, in the natural sciences, when it is
a question of continuous variables. Indeed, the arguments used
in the theory of marginal utility strikingly resemble those by
which, a couple of centuries ago, mathematical precision was
given to previously vague ideas such as mass, force, velocity,
acceleration, mechanical work, etc. — ^a precision which was only
achieved for measures of heat, light, and electricity in quite
modem times.

It should be observed, however, that the more or less
precise comparisons which we are accustomed to make nearly
always relate only to small quantities ; precisely, in other words,
to the marginal utility of the various commodities or goods.
To determine whether the consumption of a particular commodity
as a whole is productive of more or less utility, or how many
times greater or less that utility is than in the case of another
kind of commodity, is of course much more difi&cult — ^if not
impossible : a fact which can best be proved by the many
mistakes which we make when a more violent change in our
habits of life is in question. Sometimes this comparison is even.

THEORY OF VALUE 39

to a certain extent, self-contradictory, as wlien the consnmotion
of a number of (commodities such as meat and corn in the above
example) forms an inter-related whole — so that, strictly soealdiig.
one can only speak of a certain total amount of welfare w’hich
IS achieved by the combined consumption of a number of diferent
commodities.

Gra'phical Version . — If there are only two ways of using the
given stock, of goods, then it is simple to illustrate the above
argument graphically.

Let the horizontal line AB represent the original stock of
corn. On each of the successive unit lengths along this line, counted

Fia. 1.

from left to right, we erect a rectangle ; the areas of these
rectangles represent the additional amounts of utility or satisfac-
tion accruing to the colonist if his direct consumption of corn,
during the period of consumption in question, is increased to one —
from one to two — ^from two to three, etc. — units or kilograms.
The upper limits of these rectangles form a stepped line, and for
this, without introducing any material error, a continuous curve
may be substituted. The area bounded by this curve, by the
vertical line drawn through the point A, by the horizontal line
and by a variable vertical line (or ordinate) represents the whole
utihty when the consumption of grain is restricted to that part

40

LECTUEES ON POLITICAL ECONOMY

of the horizontal line which is cut bj the variable vertical line.
Ex htfpothesi, the curve gradually approaches the horizontal line
and will, sooner or later, intersect it ; for every consumption of
corn over and above a certain quantity does not produce any
extra utility.

It is clear, however, that the portions of this curve (or surface)
which are furthest to the left do not really exist, for the colonist
would starve to death if his annual ration were limited to only
a few kilograms of corn. The curve only acquires real significance
in the case of an increase or decrease of the stocks annually
consumed. With every increase or decrease by one unit, there is
a corresponding increase or decrease of utility, which is represented
in the diagram by a narrow rectangle, or — since the base of this
rectangle is one unit — ^by its height reckoned in linear units ; i.e. by
the ordinate of this curve. This, then, will be the geometlrical
representation of the mai^inal utility of the com when its
consumption per unit of time or period of consumption is indicated
by the corresponding section of the horizontal line, measured
from A.

Let us now suppose that, on the horizontal hne, we construct
a similar figure, from B, going from right to left, and draw a curve,
of which the enclosed surface and the ordinate represent the total
and marginal utility respectively, of indirect consumption of
com (m the form of meat and eggs). One unit of length on the
horizontal line will still represent one kilogram of com, and the
narrow rectangle (or trapezium) constructed upon it and bounded
at the top by the curve — or alternatively the height of the
rectangle, the ordinate of the new curve — ^will indicate the
increased utility which would arise if the quantity of corn
employed in feeding poultry were increased by one kilogram,
supposmg the colonist obtained it without cost. Since, however,
it must be taken from the stock otherwise available for direct
consumption, the actual increase of utility will correspond to
that part of the rectangle, or of its height, which is bounded by
the two curves. The new curve will obviously fall from right to
left, and should, therefore, sooner or later, intersect the old curve.
It is now easy to see that the most advantageous use of the original
stock of com wiU be found by dividing the line AB at a point C,
which lies vertically below the point of intersection of the two
curves. Here the two curves have a common ordinate, which is
equivalent to saying that the marginal utilities of the com
consumed directly, and of the com used as animal food, are
the same.

THEORY OF VALUE

41

Strictly speaking, however, our diagram only has this
significance in so far as it relates to two kinds of consumption
winch are independent of each other— the utility or satisfaction
derived from consuming a certain quantity by one method being
equally great whether much, little, or nothing is consumed by the
other method. This is never wholly the case — least of all as regards
two such closely related kinds of consumption as vegetable and
animal food. Consequently, the first curve represents the utility
and marginal utility of the direct consumption of com on the
assumption that there exists no other use for it. But the right-
hand curve would certainly have an entirely difierent shape if it
really represented a consumption of meat ictthout a simultaneous
consumption of com. It may be regarded as representing the
utihty and marginal utihty of a consumption of meat which is
carried on while, at the same Ume^ the remaining stock of corn
is consumed directly. Naturally, we might also have regarded the
meat consumption as primary and the corn consumption as
secondary. The two curves would then have assumed very
different forms, but the result, i e. the division of the original
stock of corn, would remain the same on the supposition that,
in this case, there is only one equilibrium position. But this
assumption — as we shall see later — ^is by no means always true.
(For an algebraic treatment of the problem, see p. 47 seq )

A question of great interest, not only in relation to this
special case, but for all that follows, is to what extent the
division of the original stock (of com) among various uses is
altered if, for technical reasons, the quantity of the original
commodity required for the production of a unit of the second
commodity is also altered. Let us assume, for example, that,
for the production of 1 kilogram of chicken or eggs, not 5 kilograms
but (in consequence of more rational methods of feeding or of
breeding) only 4 kilograms are necessary. In such a case, it is
evident that the quantities of com set aside for poultry food
will yield a greater utility than previously. In other words,
the curve of meat consumption (cf. F%. 1) will begin higher
up on the vertical axis than before. But, on the other hand,
the demand for meat wiU, for the same reason, be satisfied
relatively more rapidly since every unit of com used wiU bring
a greater increase of meat than previously. For this reason the
curve of meat consumption will fall more steeply than before,
and it is, therefore, not difl&cult to see that it may just as well

42 LECTDEES ON POLITICAL ECONOMY

intersect the ctnre of com consumption to the right as to the
hfi of the former point of intersection. In other words, the
technical improvements by which more meat is obtained from
every unit of com may, according to circumstances, lead either
to an increased or to a diminished direct consumption of com,
and thus to a decrease or increase of the quantity of corn
consumed in the form of meat.

On the other hand, it may be thought that, in such
circumstances, the consumption of meat must necessarily be
increased. For iE it remained unchanged or were reduced, then
in both cases more com would be consumed than formerly,
and the marginal utility of com would fall ; whereas the
mai^al utility of meat, one would suppose, would remain
unchanged, or rise. Consequently, the noarginal utility of the
latter would rise in relation to that of com, whereas equilibrium
requires that it should /oK, since more meat is now obtained
per unit of com than formerly. However, this conclusion is
only justified on the assumption that the consumption of com
and meat are independent of one another. If we make the contrary
(and more realistic) assumption, that they influence each other
to a high degree, then it is conceivable that an improvement
in the production of meat might lead to a diminished consumption.
If, for example, as we have assumed, the consumption of meat
remained unchanged and the consumption of com rose in
consequence, then, in reahty — since human needs for sustenance
are limited — ^the marginal utflity of both corn and meat would
fall, and it is, a priori, not impossible (though in this case
improbable) that the latter would decline more rapidly than the
former. We see from this what are the complications which
may emerge from analysis of the simplest possible case of
exchange, and how careful one must therefore be not to draw
hasty conclusions in the much more complicated cases arising
in a developed system of trade which will be the subject of
examination in the following pages.

The relations between two or more commodities as regards
consumption may, as Pareto remarks,^ be of two essentially
diflerent, indeed contrary, kinds. They may be complementary —
so that an addition to the one requires for its eflective utilization
an addition to the other, or others. Or they may be competitive —

^ \_Manuel d'economie politiqite, p. 251.]

THEORY OF VALUE

43

so that an addition to the one renders a part of the other, or others,
superfluous. This distinction is perfectly valid and has various
interesting consequences, though the second type is seldom found
in complete purity. In the case discussed above, the animal and
vegetable foods are largely substitutes for each other, but, on the
other hand, each also increases the satisfaction derived from the
other. Perhaps some day the physiologists will succeed in isolating
and evaluating the various human needs for bodily warmth,
nourishment, variety, recreation, stimulation, ornament, harmony,
etc., and thereby lay a really rational foundation for the theory
of consumption.

Exchange at Given Prices

In the actual exchange of goods between individual buyers
and sellers — ^and frequently enough in a larger economic unit,
or even a whole country — ^the given market price, or the world
price, has the same function as the technical rate of exchange
in the examples discussed above. It is true that the individual
who desires to make an exchange, himself exercises a certain
influence on prices by virtue of his supply or demand, but, in
most cases, this influence is, in itself, inappreciable and therefore,
from his point of view, without significance. He plans his
economic behaviour exactly as he would do if the exchange
value of the goods was unalterably given and predetermined.
Consequently, his offer of his own goods and his demand for those
of others — ^assuming the exchange to take place within a given
consumption«period — are determined in exactly the same way
as in the previous case, in which it was a question of alternative
uses of the same goods. If, for example, he has agricultural
goods for sale but wishes to buy coffee, sugar, fish, manufactured
goods, etc., he must regulate his offers and his demands in such
a way that consumption in the period in question, both of the
goods he gives up and of those he receives, will yield a marginal
utility proportionate in each case to the given exchange value
in the market for the goods in question. If, as is usual, the price
is expressed in money and if the marginal utility of each
commodity is compared with the price, then these ratios, or what
are usually called the weighted marginal utilities (weighted
according to the price) will always be equal. Hence the last
shilling which our farmer expends, whether on coffee, sugar,
clothes, or shoes, and also the last shilling’s worth of com, meat,

44 LECTURES ON POLITICAL ECONOMY

bacon, eggs, linen, wool etc., wMcb lie retains for Ms own
consumption — ^all taken on a given consumption-period, say one
year — ^will bring him the same amount of utility or satisfaction ;
for otherwise economy necessarily demands that he increase
Ms consumption of one or more of these goods, and reduce
that of others.

Moreover, this is exactly the same condition as in the
preceding case and can, especially if we restrict our observations
to two commodities only, be represented by exactly the same
diagram as before, in wMch, by the horizontal line AB (see
Fig. 1), we now represent the quantity of goods in hand at the
begiiming — or, what amounts to the same thing, their exchange
value (e.g. in money) — ^wMlst the marginal utility of the goods,
partly for direct consumption and partly in the "'converted ’’
form assumed by exchange — or the utility of the last sMlling’s
worth of each commodity — ^is represented by the ordinates
of the two curves.

Now we discover in this new case exactly the same
peculiarities and apparent paradoxes with regard to the effect
exercised by an alteration in the exchange value of goods, as
determined in the market, on the supply and demand of the
individual consumer. For example, suppose that a person has
a stock of corn and wishes to exchange a part of it for coffee
beans. If the market rate at some moment of time is 10 kilograms
of com for 1 kilogram of coffee, he will acquire the quantity of
coffee he needs for a year, or half-year, by exchanging
100 kilograms of com for 10 kilograms of coffee. But what
will happen if the relative price changes so that for 1 kilogram
of coffee he need only give, say, 9 kilograms of com ? In the
present case, wMch relates to goods wMch cannot really replace
each other in consumption, it seems probable that the change
in price must lead to an increased consumption of coffee. On
the other hand, it is uncertain at the outset whether it will
lead to an increased or diminished supply and, consequently,*
to a decreased or increased consumption, of com. For if, in
consequence of the lower price, he increases his consumption
of coffee by more than one-tenth to, say, 12 kilograms, then
he will increase the quantity of com wMch he must give in
exchange for coffee to 9 x 12 = 108 kilograms ; and consequently
he will have 8 kilograms of com less for direct consumption.

THEORY OF VALUE

45

But if lie increases Ms consumption of coffee by less than
one-tenth. — say only to 10*5 kilograms — ^then he need only offer
94*5 kilograms of com, and will consequently have 5*5 Mlograms
more than formerly to consume directly. Each is consistent with
the law of marginal utility, wMch only requires that the marginal
utility of coffee in relation to that of com shall fall until it
accords with the new relative exchange value, and tMs condition
may perfectly well be satisfied in either case. Indeed, it is even
conceivable that the new price situation might possibly lead
to a diminished consumption of coffee, in so far as an increased
consumption of foodstuffs, such as com, might perhaps i educe
the need for coffee and thereby in itself reduce the marginal
utility of coffee even although aU other circumstances remain
unchanged. This is, of course, as we have already pointed out,
still more true of goods wMch can completely replace each
other in consumption, such as the various kinds of animal and
vegetable foodstufb, etc.

The above conclusion, wMch is theoretically irrefutable,
viz. that the supply of a commodity may be either increased
or diminished when the price rises in relation to that of other
goods, and vice versa when it falls, is seldom encountered in
reality, because a rise in price nearly always leads to an increased,
and a fall in prices to a diminished, prodiuiion of the commodity
in question. If this change in production cannot be effected with
sufficient rapidity, or not at all — or if, as we shall show later,
the two commodities are made from wholly different factors of
production — ^then there is nothing to prevent such a result,
though it is generally regarded as unexpected and paradoxical.
Thus, for example, a chance rise in the price of agricultural
products may very well induce farmers who had previously been
compelled to deny themselves necessaries in order to pay interest
and taxes to increase their consumption of the produce of the
land, with the result that, in spite of the rise in price, less of
those products, instead of more, will be offered on the market.
If I am not mistaken, this actually happened in the later years
of the world war.

Another very interesting case is that of the supply of labour,
in so far as the regulation of hours of labour lies in the hands
of labour itself. An increase in wages may cause more labour
to be offered in the market, but it need not necessarily do so.

46 LECTURES ON POLITICAL ECONOMY

As we liave already pointed out in connection with the
consumption of goods, both possibilities accord with the principle
of marginal utility : the labourer, if free to choose, extends his
working day up to the point at which the effort of the last hour
of labour approximately corresponds to the gain he expects from
the wages offered for that hour. If wages are raised, it might
be supposed that the prospect of increased well-being would be
an inducement to greater effort ; but, on the other hand, since
the wages for each hour are raised, the whole standard of living
of the labourer is changed. He can now satisfy his usual needs
by less work than formerly, and the increased well-being which
is now available to him can be realized in part by allowing
himself more leisure and recreation than formerly. The vehement
disputes often heard, as to whether a workman is made more
diligent’’ or “more lazy” by higher wages, cannot therefore
be settled a ^priori either way. On the other hand, there can be
little doubt that a percentage increase of wages for overtime
leads to an increased supply of labour. For, in this case, the
economic position of the workman remains essentially the same,
and the increased -wages for the last hour of work (overtime)
will therefore have their full effect. This method of stimulating
the worker to increased effort is, therefore, just as popular among
employers as it is regarded with suspicion by the workers, because
at jSrst it is a temptation to over-exertion and then later it leads
to periods of unemployment. A quite different question, of great
practical importance, though we cannot pause to discuss it now,
is whether higher wages may lead to greater intensity of work,
by enabling the labourer to procure for himself better nourishment
and a better technical education for his children, etc.

Algebraic Version . — ^It is now many years since the first
attempts were made to express economic quantities and their
relations in algebraic terms. After a period of poor success, the
method has now become fairly well established in economic theory
— chiefiy as a result of the work of Jevons, Walras, and their
followers. In what follows, we shall apply this method side by
side with our ordinary discussion, and shall introduce it here for
the first time.

If we suppose the consumption of each particular kind of
commodity to be independent of every other simultaneous
line of consumption, then we may regard the utility to a consumer

THEORY OF VALUE

47

arising from tiie consumption of a given quantity, a, of tlie com-
modity (A), during a given period of consumption as a function
f(a) of the quantity, a function about which one can only say
a ^priori (i.e. without a special investigation of each particular
case) that it increases simultaneously with a but less than pro-
portionately. If the quantity consumed is increased by a small
addition, Aa, then the total utility or satisfaction is increased by
a corresponding amount, which we may designate Af{a), The
additional utility which arises when the quantity of the com-
modity is increased by one unit, i.e. the marginal utility, will

then be expressed by the ratio H we now suppose these

quantities to become infinitesimal, the ratio wiU, as a rule, have a
determinate limit which is the differential coefiScient, or the first
derivative of the function, /(a), with respect to a. The latter,

which is usually indicated by or by/'(o), is itself a function of

da

a, and, in the present case, has the characteristic peculiarity of
being a diminishing function of its variable, i.e. it diminishes
when a increases. All this is, of course, only a symbolic expression
of the theoretical argument already developed that the marginal
utility falls — ^whilst the total utility obviously continues to grow,
though in a diminishing degree — ^when the quantity consumed,
per unit of time, increases.

If we now apply the above argument to all the other kinds
of commodities, {B), (C), (D), etc., some of which the consumer
possesses at the outset, and the remainder of which he acquires
by means of exchange at market prices, then we can express
symbolically the conditions of equihbrium for the economy of the
individual which have been described above ; on the one hand,
the marginal utility of each commodity is proportionate to its
price, and, on the other, the total exchange value of the com-
modities given up is identical with the total exchange value of
the commodities acquired. If the market prices of a unit of each
of the various goods (calculated, for example, in money) are par
Pbf Pey ^tc,, and if the quantities of these goods, which the person
in question possesses after the exchange, whether he has acquired
them or has possessed them from the beginning are expressed by
X, y, z, etc., then, if ^ ( ) and tjj ( ) indicate utility functions
analogous to/ ( ), the first condition will be expressed as follows : —

f'{x ) : ^'(y) : tp\z) : . . . = .

This is evidently equivalent to a system of equations whose

48 LECTUEES ON POLITICAL ECONOMY

Euniber is out less tiian the ntuiiber of goods dealt in. The
second condition we may simply expre^ by the equation

in wMch a, 5, and c are the quantities of the various kinds of
goods possessed at the beginning (some of which may, of course,
be equal to zero). In other words, the value, in money, of the
possessions of the person in question is the same before and after
the exchange. Consequently the number of equations is equal
to the number of unknowns — y, z, etc,, and the problem should
be capable of a mathematical solution if the forms of the functions
~/( h )> )> — ^^kich express total utility, and whose

derivatives express the marginal utility for a given consumption
of each and every kind of goods by the person in question, are
precisely known. A closer study of the forms of these functions
falls within the province of experimental psychology and
of statistics of consumption ; it may perhaps be of great
importance in the future. For the present, we are only concerned
with the attempt to investigate the inter-connection between the
phenomena of consumption and exchange, and for this purpose
we may be content with a general knowledge of these functions
derived from our daily experience.

In reality, as we have frequently pointed out, the position is
that the utilities and marginal utilities of the various kinds of
goods are not independent but, on the contrary, influence each
other in a greater or lesser degree. The only really rational
procedure is, therefore, to regard the total satisfaction or well-
being as a function of all the quantities of goods consumed
simultaneously per unit of time, or during a certain consumption
period, so that, if these quantities are a, b, c, etc., the function
can be symbolically represented by F {a, b, c , , Of this
function it may generally be asserted that it increases as soon as
any of the goods consumed increases in quantity, the other
quantities remaining unchanged, although, of course, in this
case a fortiori the function increases in a much smaller pro-
portion than the quantity of the single commodity. If, for
example, the increase consists of one unit of the commodity (A),
then the increase in utility (or marginal utility) of commodity {A)
should be symbolically expressed by the first partied derivative

0

of the function F ( ) with respect to a, i.e. F {a, b, c,) or, as it is

oa

frequently written, F^ (a^ b, c), which wiU thus be itself a function
not only of the quantity a, but also of aU the quantities of goods
consumed. The same applies to the marginal utility of the goods

THEORY OF VALUE

49

(R), (0), etc. Thus, according to this view, the conditions of
equilibrium would be that the partial derivatives of the total
utility functions with respect to the quantities y, 25 , etc., available
for consumption, should after exchange be proportional to the
prices of the goods. Thus : —

: Fy . Fg : . . , ^ pa * Ph Pc • • •
to which must be added the same equation as above : —

Pa^<^ + Pb-y+Pc-^+ • - • = Pa*«+B-^+i>c-C+ . . ‘

which means that the total money value of the goods in the
possession of the person is the same before and after the exchange.

C, Isolated Exchange

Before proceeding to show how the exchange values of
goods, which we have hitherto regarded as data, are in reality
determined by the competition of buyers and sellers in the
market, we shall refer briefly to a kind of exchange whose direct
practical importance is not as great as its theoretical interest :
exchange between two isolated individuals. In reality, an
exchange between two individuals is almost always effected
imder the influence of the market, even if not in the market
itself. For the moment, however, let us abstract from this,
and assume that, during the period of consumption in question,
neither of the parties has any opportunity of trading with anyone
but the other party. The problem of price formation in this
case is far from being as simple as it may at jBrst sight appear.
We shall not treat it in more detail than is necessary to show
by contrast the influence of competition on prices.

Let us suppose that a peasant from the plains and a peasant
from the forest meet on the way to town. The former has a sack
of com which he has so far been unable to dispose of, the latter
has half a load of wood which he intends to sell. Since each
needs the goods of the other, they agree to exchange, and each
of them is thereby saved an extra journey to the town. It nmy
be that, if necessary, the peasant from the plains would give
his sack of com for a quarter of a load of wood ; and the peasant
from the forest, on his part, his half -load of wood for only half
a sack of com. Thus, if they exchange only with each other,
they both consider that they have made a considerable gain on

50 LECTURES ON POLITICAL ECONOMY

tte exchange ; but they might equally well have exchanged their
stocks if the one had possessed If sacks of com or if the other
had had three-quarters of a load of wood, and so on. Again, if
we suppose that the stocks in their possession had been greater
and that they had only this one opportiinity for exchange
during a longer period of consumption — e.g. for a whole year
in advance — ^then it is quite clear that the question how large
a quantity of their respective goods they could and, from an
economic point of view, should, exchange with each other is
quite indfierminate. Within certain more or less wide limits,
the question may be answered in an infinite number of ways,
since it is only a question of satisfying the condition that the
exchange shall benefit both parties ; and here there is no other
necessary condition. So much only is certain, that if the exchange
continues until equilibrium is reached for both parties, the
relation between the marginal utilities of the com and of the
wood must be the same on both sides : —

marginal utility of 1 unit of com _ marginal utility of 1 unit of corn
marginal utility of 1 unit of wood marginal utility of 1 unit of wood

(for the peasant trom the plains) (for the peasant from the forest)

Otherwise — ^at least theoretically— the exchange would proceed
further ; or, alternatively, it would already have proceeded too
far — ^in which case it would be to the advantage of both to
re-exchange a certain portion. If, for example, after the peasant
from the plains has exchanged a certain quantity of com for
a certain quantity of wood, it is more or less a matter of
indifierence to him whether he obtains two more logs of wood
of ordinary size in exchange for 1 litre of com, whilst the peasant
from the forest still considers it advantageous to obtain in
exchange a few more litres of com at three or four logs of wood
per litre, then the latter should, by offering this price, or one
near it, be able to induce the other party to continue the exchange ;
and so on.

But this is by no means the same thing as saying that the
relation between the marginal utilities of the two commodities
(which, in equilibrium, should be the same on each side) will be
also the same as the proportion in which the whole quantities
exchanged stand to each other and which, therefore, constitutes

THEOEY or VALUE

51

the average ratio of exchange of these goods. In fact, this ratio
can, within certain, limits, vary indefinitely, and in each particular
case the relation between the marginal utilities of the goods at
the margin of exchange will be difierent, though always the same
on both sides for the persons exchanging.

It is a pretty mathematical problem — ^which we will not
pursue here — ^to investigate the law which these variations
follow.^ Here we shall content ourselves with establishing the
fact that price determination in isolated exchange is an
indeterminate problem ; i.e. it cannot be solved solely on the
assumption that both parties desire the greatest possible profit.
This is a point whose great importance — even in practical affairs
— ^we shall subsequently realize. VTienever isolated exchanges
occur in practice, the actual determination of price will depend
in a high degree on the personal characteristics of the contracting
parties, their cunning and coolness, or on mutual goodwill, all
of these being things intrinsically too complex and variable to
be embodied in the schematic presentation of economic theory
to which we must here confine ourselves. Certain related or at
least analogous cases (where not two individuals, but two great
organizations of buyers and sellers, or employers and employed,
are opposed to each other) are evidently of the utmost practical
importance ; and it is, therefore, essential that the economist
should clearly understand the extent to which his science can
afford him any guidance in answering these questions.

One of the greatest difficulties with which the arbitrators
between employers and employed have to contend is the absence
of any scientific standard for the amoimt of wages or profits
in a big conflict. What is usually called a reasonable wage, or a
reasonable profit, proves on investigation to be not so much
reasonable as usiial, to be in fact the wage or profit determined by
free competition under the prevailing conditions of time and place.
If, therefore, the conflict only extends over a small area, such as
a single factory, then the arbitrator has sufficient basis for his
decision in the wages and conditions prevailing in other establish-
ments in the same industry. But this is not the case if, as is
more and more common in modern collective bargaining, a wage
dispute rages simultaneously throughout the whole of an industry,
or even a connected group of industries.

^ This problem was first treated by Edgeworth (see Marshall, Principles,
4th ed., appendix, note xn {his) and my Vber Wert, etc., p. 36).

62

LECTUEES ON POLITICAL ECONOMY

B. Price FormMim in the Open Market. Exdmnge of two

Gomnodities

The more or less jSxed ratios at wMch. goods are exchanged
on the market (usually by means of money) are not, as is often
supposed, due to qualities inherent in the goods themselves ;
nor, at least directly, to their normal costs of production. "As we
have already indicated, they spring from the nature of exchange
on a market (as opposed to isolated exchange) ; from what
Jevons called ‘‘ the law of indifference ”, which is, fundamentally,
nothing else than the old “ free competition

According to this law, there cannot theoretically be more
than one price in the market for the same commodity at the
same time, or more than one ratio of exchange between two
commodities. But in that case, it may be asked, could not the
sellers ” (the holders of a particular commodity) hold back
their supply at the beginning, thereby forcing up prices, and
then afterwards lower them in order to dispose of the remainder
of their goods, or so much of them as they do not wish to retain ?
Of course they could, and they often do. But there is always
the risk that some sellers may succeed m disposing of the whole
of their stocks while the price is still high, so that the others
will either not be able to sell their goods at all or will have to
be satisfied with a price much lower than they would have got
if the equilibrium price had been fixed by competition from
the beginning ; since the purchasing power of the buyers who
had already partially satisfied their needs at the higher price
would then be less than it would have been if, from the
beginning, they had bought the same quantity at a lower price ;
or since as a rule there would then remain fewer buyers able to
purchase the goods. This is presumably the reason why so-called
rings or cartels of producers or other sellers so often fail, when
the participants have only agreed to maintain a high price,
but have nothing else in common and have no organization
controlling output and individual sales. If, on the other hand,
organization has reached the point of forming a cartel or trust
in the real modem sense, so that the ma yiTunTn quantity of
goods which each of the members may offer is determined
beforehand ; or if the members agree to compensate each other
for possible losses, or to divide their profit# or simply to set

THEORY OF VALUE

53

up joint production or a joint selling organization under single
control, then price formation will more or less approximate to
monopoly conditions — of which we shall have more to say later.^
Assuming that buyers (i.e, holders of the other goods) also
combine, form trusts, cartels or rings, then there is no longer
any purely economic law of price-formation — ^no law based on
mutual desire for the greatest possible gain — and we revert to
isolated exchange, in which, as has been said already, all possible
rates of exchange are, within certain limits, conceivable.

If, however, we disregard this possibility and assume
universal free competition, then, so far as genuine market
transactions are concerned, the relative prices of commodities
will more or less rapidly approach a certain equilibrium position,
or else oscillate about it. At this equilibrium position, all holders
of goods will be able to exchange up to a point of relative satiety,
that is to say, they will continue to exchange so long as there
is any advantage in doing so at that market price. We may
assume, for the sake of simplicity, that this equilibrium price
will be reached at the very outset. For the individual desiring
to exchange his goods, the price relationships thus reached in
the market will have exactly the same significance as the given
prices in the case we discussed above.^ He will regulate the
supply of his own goods and his demand for other goods in such
a way that the marginal utility of each commodity will be
proportional to its price, or that the weighted marginal utility
is everywhere the same (in other words, that for the last s hil l in g
he spends he will obtain the same additional utifity from each
commodity). To every price relationship, therefore, there
corresponds for each individual a determinate combination of
supply and demand, and of quantities of goods retained and
acquired. The sum of the individual demands for each particular
commodity evidently makes up the total market demand for
the goods and, in the same way, the sum of the individual
supplies constitutes the total supply of these goods. Market
equilibrium is thus only possible with a price relationship at

1 It is related somewhere in the Corpus Juris how two teachers of grammar
in a small Roman town, instead of entering into mutually injurious competition,
agreed to divide the profits of their lessons. On the same principle innumerable
agreements have been entered into, in ancient and modem times, between
sellers of all kmds of goods.

2 [See page 43 seq.]

54

LECTURES ON POLITICAL ECONOMY

wMcli the demand and supply are equal for each particular
commodity. If we include in the demand for a commodity the
quantities which a seller wishes, at a given price, to retain for
his own use, then it may be said that equilibrium is to be found
in a system of prices which, for each commodity, makes the
demand equal to the stocks in the market, or to the total supply
of that commodity. Thus, on the assumption that the market
gravitates quickly enough towards equilibrium, it should be
possible — ^if the given quantities of goods on the market for
a certain period of consumption, and if the personal dispositions
of all consumers, were known — ^to establish a system of logical
relations (or what in mathematics is known as a system of
equations) from which both the quantities of goods acquired or
given up by each individual and also the relative equilibrium
prices, would be determined. It is, however, in no way excluded
— as we shall soon see — ^that the problem may, under otherwise
identical conditions, have more than one solution.

Formally, indeed, this doctrine is only a repetition of the
old thesis that the market price of goods is regulated by an
equilibrium between supply and demand. In reality we have
advanced considerably, for we have found in marginal utility
the general principle which governs supply and demand imder
any price system. We are, therefore, in a |)osition to carry the
discussion of price formation in the open market considerably
further than the earlier economists were able to do.

In accordance with our method of proceeding from the
simpler to the more complex, we will begin with the case in which
only two commodities are exchanged in the market. This case,
moreover, is not so abstract and unreal as may at first sight
appear. It is true that two particular commodities are very
seldom exchanged directly. Nearly all actual exchanges are
effected indirectly, through the mediation of money. Every
commodity, or group of commodities, has its special market,
in which it is exchanged for money, and the market price of
this commodity is determined there with more or less regard to
the simultaneous market prices of other commodities. But if
we look at the problem broadly and consider, for example, the
economic interests of a particular class of society, of a district,
or country, as compared with those of other classes, districts, or
countries, then it not infrequently happens that, omitting

THEORY OF VALUE

intermediate links, we must regard as decisive the exchang

only two commodities, or of two related classes of commodil

whose price-ratio is determined almost without reference to
other goods on the market, which are of comparatively minor
importance. This is true where the interests of an agricultural
population are opposed to those of an industrial population ;
where the commodity labour is confronted with the
commodity means of subsistence ; or where the economic
welfare of a district or of a whole country depends on the price
of its staple commodity in foreign markets in comparison with
the price of its imports taken as a whole.

From the theoretical point of view, the exchange of two
commodities has this peculiarity — ^that it is the only form of
exchange which can normally take place by the direct barter
of goods against goods. Not that two holders of the different
commodities could always satisfy one another’s needs by
themselves — ^for this, in fact, occurs only in exceptional cases.
As a rule, at least one of the parties to the exchange is compelled
to deal with more than one holder of the commodity he wishes
to acquire. But, nevertheless, it should in this case be possible
to exchange goods for goods without the mediation of either
money, credit, or any other intermediary ; that being usually
— as we shall soon see — ^an essential condition for the achievement
of equilibrium as soon as the number of goods in the market
exceeds two.

We assume, for the sake of simplicity, that at the outset
the two commodities are held by different parties, so that no
one at first possesses more than one commodity. Let us suppose
the prices of the two commodities (A) and (B) offered in the
market to be expressed in terms of one of them, (-4), so that
the price of a unit of (A) is, consequently, invariably equal to
1, and the price of a unit of (B) (which we indicate by p) is
variable ; it then follows, from what has been said above, that
an arbitrary price (p) quoted in the market will call forth from
each holder of the community (A) a certain demand (x umts)
for the commodity (B), and a corresponding supply of the
commodity (A), which wall then clearly equal p>x umts. The
sum of all these demands (x) constitutes the total demand X for
the commodity (B). which implies a corresponding supply, pX,
of the commodity (A). In the same way, the holders of the

56 LECTXJRES ON POLITICAL ECONOMY

coixuncwiity (5) oSei, at the price a total supply, Y, of the
commodity (B) and demand a corresponding quantity, p.Y,
of the commodity (A). The condition of p being the eqmHbrinm
price is that the supply of and demand for the commodity (B)
are equal, so that 7 = Z ; from which it follows that demand
for and supply of the commodity (A) will also be equal, for it
follows that p.Y ^ p.X. Further, let all conceivable values of
p, which, as we have explained, must be treated as a variable,
be represented by distances from a fixed point (the origin) along
the horizontal axis, and through each of these points draw
a vertical line, on which are marked off two lengths, one
representing the total demand for (B) on the part of the holders

Demand (Supply) of
Commodity B.

of (A), and the other the total supply of (B) by the holders of
(B), We shall then obtain two connected curves, one of which
represents the demand for (B) and the other its supply for every
conceivable price-ratio. If these two curves intersect and so
have an ordinate in common, then at that point demand and
supply are equal ; and the corresponding distance along the
horizontal axis (the abscissa of the point of intersection) represents
the desired equilibrium price.

If we begin by assuming that (A) and (B) cannot in any
way replace each other in consumption, we can then describe
the general course of these curves in the following way. If p = 0
— ^i.e. if (B) can be obtained for nothing or for a purely nominal

THEOEY OF VALUE

57

amount of (A) — every Koider of (A) will demand (B) up to the
point of complete satiety — i.e. until its marginal utility has fallen
to zero. For this to happen, as a rule, only a finite, though
sometimes a quite considerable quantity of {B) is required ;
hence the demand curve leaves the vertical axis at a finite
distance above the origin. If p rises, the demand falls
continuously ; since the marginal utility of (J5), relative to that
of {A), must fall pari passu with its price. The curve therefore
falls continuously towards the tr-axis (though it may be convex
or concave to the ir-axis or alternately the one and the other)
and finally meets it at a point corresponding to the price at
which (B) ceases to be demanded by the holders of (A). This
point may possibly be so remote that it does not, in practice,
exist — ^ia the case when {J5) is an absolute necessity of life which
would be in demand at any price.

The supply curve of {B) follows an entirely different course.
If the price of [B) is zero, or very low, then there is no inducement
for holders of (5) to offer their goods, and when they do begin
to do so it will, at first, be only in very small quantities. The
supply curve wiU thus begin at a point on the horizontal axis
which is at a certain distance from the origin and will gradually
rise pari passu with the rising value of p. But the increase in
supply will not continue indefinitely ; sooner or later a point
will be reached at which an increased price will no longer induce
holders of {B) to offer any more, but will, on the contrary, make
them offer less, because at this higher price they can obtain
with less sacrifice of (jB) so much of {A) that its marginal utility
will fall until it is equal to the marginal utility of (J3),
notwithstanding that the latter will also sink when the quantity
of (B) retained is increased. The supply curve thus reaches
a maximum, from which it falls again towards the horizontal
axis ; however, it never cuts the horizontal axis, but moves
towards it asymptotically ; for however high a price a person
is offered for the commodity in his own possession, he will
always be prepared to give up some small part of it in order
to acquire other goods. ^

^ On the above assumption that the two commodities are independent of
each other as regards consumption, the supply curve is subject to the further
condition that the rectangle formed by the co-ordinates (i.e. the supply multiplied
by the correspondmg price) must continuously increase, since it evidently equals
the demand for the other commodity {A ), and this demand increases continuously

68

LECTUEES ON POLITICAL ECONOMY

If we now remember that, on our assumption, the two
curves are entirely independent, since the demand for and
supply of (B) proceed from different persons— the supply curve
is determined exclusively by the availability of (B) and the
demand curve by the availability of (A ) — ^then it is clear that
there are as many possible kinds of equilibrium as there are
possible kinds of intersection, for two curves drawn in the
manner we have described. The point of intersection may lie
to the left of the highest point of the supply curve ; this is the
case which was considered almost exclusively by the older
economists. In such a case equilibrium is necessarily stable,
for a slight increase of price would increase supply and
simultaneously decrease demand ; a slight fall in price, on the
other hand, would increase demand and decrease supply, so
that, if the price were by chance to be disturbed, it would
automatically revert to its former position.

But the point of intersection — ^for the moment we may
assume that there is only one — ^might also lie to the right of the
highest point of the supply curve, so that equilibrium in the
market would only be reached when supply had begun to be
restricted by the rising price. This equilibrium is also stable ;
if in this case the price rises, then supply wdl indeed be reduced,
but demand will be reduced even more, so that it will be less
than supply — ^with the result that the price must fall again.
If the price falls, then supply will increase but demand will
increase more rapidly, for which reason the price will soon
revert to its former level.

when the pnce of (B) in tenns of (A) increases, and consequently the price of {A)
in terms of {B) falls. If, on the other hand, the two commodities are to some
extent substitutes, this condition need not be satisfied ; for, in that case, a
falhng price of (A) in terms of {B), and accordingly a rismg price of (B) in terms,
of (A), might conceivably cause a diminished demand for (A) and, accordingly, a
still greater diminution in the supply of (B). It should be observed, moreover,
that the rising portion of the supply curve may be absent if the commodity
offered (B) has no appreciable utihty for its holder, which is often the case with
goods which are manufactured only for sale. In that case, the commodity (B)
IS offered — ^unless there is the possibility of withholding it until the market
position is more favourable — ^to the maximum extent and at any price, so
that the supply curve at the beginning is represented by a straight Ime parallel
to the price axis, which later becomes a falling curve. As may easily be seen
from what has been said, in such a case the demand curve for (A) — ^whose
abscissae thus represent the price of (A) in terms of (B) — ^will, in its lower
course, become a rectangular hyperbola, with the axes as asymptotes, and
will, therefore, not intersect the price axis. Holders of (J5) will th^ demand (A)
at any price of (A), though naturally in quantities which stand in inverse
proportion to the price.

THEORY OF VALUE

59

That the older economists so generaHv neglected this case —
except occasionally in regard to foreign trade — ^is all the more
remarkable, since it is evidently in full agreement with the well-
known and frequently observed fact that the demand for a com-
modity which has risen in price (e g. sl necessity) may frequently
fall in a lesser proportion than the actual rise in price. As against
this particular commodity all other commodities constitute a
group whose relative price has fallen. Their supply (in exchange
for the former commodity) has, on the other hand, clearly risen ,
it thus rises with a falling price and falls with a rising price of
that group of commodities (expressed in terms of the former
commodity), and in one of these positions equilibrium between
demand and supply will be reached.

Finally, there is nothing to prevent the two curves having
several points, and (if so) at least three, in common. In this
case, the curious position arises that both the point of intersection
to the extreme right and that to the extreme left indicate a stable
position of equilibrium, whereas at the intermediate point of
intersection a so-called unstable equilibrium prevails ; the
equality of supply and demand at this price is merely accidental.
A disturbance of the price equilibrium in this case has no tendency
to an automatic restoration but, on the contrary, produces an
uninterrupted shifting of the price in one direction or another
until stable equilibrium is reached at one of the two extreme
points of equilibrium either to the left or the right.

This very remarkable phenomenon was first pointed out
and analysed in detail by Walras.^ Walras himself, however,
seemjs inclined to under-estimate its practical importance, and
appears to be of opinion that, imder actual conditions, where
a large number of articles are exchanged for each other, only
one position of equilibrium would really be possible in the same
market. But in that he is mistaken. We have already seen
examples, derived from exchanges between employers and
employed and between farmers and industrialists — and we shall

^ In Marshall’s Principles (4th ed., p. 525, et seq.) there are curves of
supply and demand which resemble those discuss^ here. They relate, however
to a different case, namely the number of positions of equilibrium which with
an unchanged (or only slightly changed) disposition on the part of the buyer
might occur as regards such commodities as follow the so-called law of increasing
returns ; commodities which can be produced and sold at a lower cost, if the
output is large than if it is small ; e.g. newspapers, books, railway journey
and others.

60 LECTUEES ON POLITICAL ECONOMY

later add a famous case of intematioiial exoliaiige — wMch. stow
that equilibrium may very well occur under circumstances
where a price increase would cause a reduction and not an
increase of supply, and vice versa a reduction of price an increase
of supply. Rom this it is only a short step to the admission
of several possible equilibrium prices in the same market, as
a glance at Fig. 2 will show.

We arrive at still more remarkable results if we assume,
in accordance with what often occurs, that the two commodities
may, to a greater or lesser degree, be capable of acting as
substitutes. In that case, as we have already indicated, the
demand curve of either commodity may also have both a rising
and a falling section and the chances that both curves will have
several points of intersection, or even that they may approximately
coincide over small stretches, are quite considerable. It is not
impossible that puzzling disturbances in the market, which
frequently occur without any known cause, may be properly
attributed to the hitherto neglected fact that a particular state
of equilibrium may not be the only one which is possible imder
the given conditions, and that a state of equilibrium chosen at
random can just as well be unstable as stable, or may for some
insignificant reason be converted* from one into the other.

An admittedly artificial example of this (cases more or less
similar to which are, perhaps, not so rare in reahty) is the
following : —

A person, possesses a stock of wheat, another person. By
a stock of rye. For the sake of simplicity we wiU assume that rye
and wheat have the same nutritive value per pound (this, however,
is not essential to our argument). We assume, however, that
wheat (owing to its better taste) is preferred by both parties ;
yet each of them endeavours primarily to obtain the maximum
riourishinent'y but only up to a certain limit, say a thousand pounds,
beyond which any additional nourishment cannot in general be
utilized and is, therefore, without value. If jd at the beginning
had 800 lb. of wheat, then, as the price of rye varied, his demand
for rye would clearly be determined in the following manner.
If the price is zero, i.e. if rye can be obtained for nothing, he wiU
provide himself with 200 lb., neither more nor less, because this
will fully satisfy his requirements for this kind of nourishment.
If the price rises above zero he will be compelled, in order to
acquire the necessary nourishment, to dispose of a part

61

THEOEY OF VMiUE

of HIS stock of wkeat, but in that case be will evidently be
forced to consume more rye than before. In other words, bis
demand for rye will increase wben tbe price of rye increases. If p
is tbe price of rye, expressed in w’beat (or in tbe money price of
wheat as a unit), then, as will easily be seen, bis demand x will
be such that it satisfies tbe equation

800 + a; — p.a; = 1,000,

so that

X =

Tbe limit is reached wben p

200

l-^p

4

equals wben be will have to
D

Demand (Supply)
of rye.

Fig. 3.

exchange tbe whole of bis stock of wheat, 8(X) Ib., in order
to get a sufficient amount of nourishment, i.e. 1,000 lb. of rye.
If tbe price of rye rises still further be cannot in any way acquire
full satisfaction, but will endeavour to obtain as much as possible,
which be will do by continuing to ofier tbe whole of bis wheat for
as much rye as tbe market determines. His demand for rye will

thus now = — . Only wben p = 1, and rye consequently

commands tbe same price as wheat, would an exchange be
purposeless for him. At this pomt be ceases to demand rye.

His individual demand curve will thus assume tbe following

62 LECTXJEES ON POLITICAL ECONOMY

form : it begins at a point on the vertical axis, the distance of
which from 0 corresponds to a demand for 200 lb. of rye. It then
describes an hyperbola which has for its asymptotes (a) the
horizontal axis and (b) a vertical line which intersects the horizontal
or price axis at a distance of one unit from the origin. This hyper-
bola, however, terminates at a point whose distance &om the
horizontal and vertical axes corresponds to a demand of 1,000 lb.,

or a price of rye, p =

4

‘ 5 ^

The demand curve next describes a

descending hyperbolic curve, whose asymptotes are the horizontal
and vertical axes. At a distance, along the horizontal axis the
curve suddenly descends from a height, corresponding to a
demand of 800 lb. rye, towards the horizontal axis.

The amount of rye offered by B will clearly depend on the
size of the stock he holds. We will assume that it is exactly
1,200 lb. If the price of rye is zero he will, of course, have no
inducement to exchange ; but as soon as rye, expressed in terms
of wheat, is worth something, however little, he will immediately
exchange the whole of his worthless surplus, 200 ib., of rye in
order to obtain at least some wheat. If the price of rye is raised,
he will be m a position to acquire more and more of the desired
commodity wheat, and in order to obtain as much as possible
he will still continue to offer so much rye that his total stock of
food will amount to exactly 1,000 lb., neither more nor less.
If we call his supply of rye y we shall arrive at the equation : —

1,200 + f-y — y= 1,000

where y -

200

—or exactly the same as we previously fotmd for

1-3?

A"s demand for rye. The only difference is that P’s supply of rye

4

will continue to increase, even after the price reaches ~ ; for so

0

long as wheat can be obtained in the market there is no reason
why B should not procure more than 800 lb. of it. Only when

5

the price of rye has risen to ~ of that of wheat can B, who at that

o

price will offer the whole of his stock, 1,200 lb., no longer increase
his supply, and indeed has no reason for doing so, since at a
higher price he could obtain the necessary 1,000 lb. of wheat
even for a fraction of his stock of rye.

In this case, the curious fact emerges that the supply and
demand curves of the two individuals coincide for a large part
of their course. In other words, for every price of rye between

THEOEY OF VAIUE

63

zero and A’s demand for rye and B’s oSer of it are exactly
0

tile same — and consequently, for the same reason, their respective
supply of and demand for wheat.

This example should show to what a large extent the simple
scheme of the variations of supply and demand with which
economists have hitherto contented themselves, requires to be
developed and completed in order to correspond with the varying
phenomena of reality.

E. Continiiation. Exchange of Three or More Commodities

As soon as there are more than two commodities on the
market, complete equilibrium cannot as a role be reached by
direct exchange alone, but indirect exmange must supplement it.
This is seen in its simplest form in the extreme case where
direct exchange is altogether excluded. A country (say Sweden)
has timber for sale and sufficient corn for its own needs, but must
buy fish. Another country (Norway) can supply fish and has
sufficient timber, but must buy com. Finally, a third country
(Denmark) has a surplus of com and sufficient fish, but lacks
timber. Evidently no direct exchange can take place here, but
an indirect exchange may ; if, for example, Denmark as an
intermediary buys up Norway’s surplus of fish in exchange for
its own surplus of corn, in order, in its turn, to sell the former
to Sweden and thereby satisfy its own requirements for timber.
Or the same result might have been achieved by the use of
a special medium of exchange, money or credit, as we shall
soon see.

But even if , in a three-cornered exchange, each party was
a purchaser of the products of both the others (so that, up to
a point, direct exchange could take place) even then, so far as
the exchange values of the goods were regulated only by mutual
supply and demand in direct exchange, a final price equilibrium
would not, as a rule, be reached. As between each pair of
commodities, the price ratio would be determined in a separate
market, isolated from the other two, and the resultant three
relative prices would not usually be correlated, i.e. they would
not be such that each would be the ratio (or product) of the
other two. If, for example, in a direct exchange of the commodity
(jB) (fish) for the commodity ((7) (com) the equilibrium price were

64 LECTURES ON POLITICAL ECONOMY

sTicli that one unit of (B) were exchanged for two units of
(0), and on the market for (C) and (A) (wood) the price is four
units of (C) for three of (A), then if the prices are correlated, two
units of (J3) must be exchanged for exactly three units of (A).
It may, however, happen that, in the direct exchange of (A) for
(B), a different equilibrium price would obtain, so that either
less (say one and a half) or more (say two and a half) units of
(B) would be exchanged for three units of (A). Whichever
occurred, it would then be profitable to enter into a so-called
arbitrage transaction* Thus, in the latter case, a holder of (A)
desiring to acquire (0) would first buy a suitable quantity of
(B) and subsequently exchange that (B) for (0). In this way
he would obtain five units of (C) for three of (A), whereas by

u

o

O

Pig. 4.

direct exchange he would only have obtained four units of (C),
and similarly if the price of (B) in direct exchange for (A) had
been lower than the correlated price. If, therefore, full
equilibrium is to be reached in such cases, at least a part of the
commodities in the market must necessarily be the object of
indirect exchange.

The commonest procedure in such cases is for the exchange
to be effected with the assistance of a special medium of
exchange, money, which only formally appears in the market
as an object of exchange. In the extreme case which we
mentioned by way of introduction, Sweden, for example, buys
fish from Norway for rmney ; Norway uses this money to buy
corn from Denmark, and Denmark in turn uses it in payment
for timber from Sweden, so that in the end Sweden gets its

THEOSY OF VALUE

65

money back. VTe can visualize the position by means of a diagram
in whicb eacn commodity moves one-tliird of the circumference
of an outer circle, whilst money makes a whole revolution in
the opposite direction in an inner circle, and thus finally returns
to Us starting poird. The result is. or may be, that after the
conclusion of the business only the goods have changed hands,
whilst the sums of money employed are in exactly the same
hands as at first. Thus, in fact, goods have been exchanged
for goods, not directly, but, in part at least, indirectly. The law
of marginal utility has been none the less effective. Under
ideal market conditions, in which the final price equilibrium
is established from the very beginning, the exchange values and
the marginal utilities of all commodities must be proDortional
for each of the exchanging parties taken separately. As far as
money is concerned, as we have said, its role is purely formal —
or may theoretically be conceived as such. Indeed, a sum of
money, however small, may effect an indefinitely large exchange
of goods, if it circulates frequently between the exchanging
parties. The importance of this observation will become clear
when we come to treat of the functions of money. However
simple and co mm onplace the above consideration may appear, it
constitutes in reality the master-key to a proper understanding
of the peculiar problems of money.

It is not easy to give a graphical version of this problem —
exchange that, in part at any rate, Is indirect. If there are only
three commodities, then it is possible to represent the position
by a three-dimensional figure — we want to do so — ^but even this
method breaks down when the number exceeds three.

On the other hand, we can easily express the conditions of
equilibrium by algebraic symbols and thereby set out the logical
relations or equations which determine the equihbrium price. It
is simplest to conceive demand in the wider sense already mdicated,
including the quantities of the varioi^ goods which the original
holder wishes to retain for his own consumption at a given system
of prices. In equilibnum, demand in this sense must be equal,
not to the amount offered in exchange, but to the whole of the
stocJcs available in the market for consumption in a given period.
Of course, we might have used this method for two commodities ,*
and this would have given us a more satisfactory expression of
the position where, for example, one person is in possession of
both of the traded commodities from the start, and appears

66 LECTURES ON POLITICAL ECONOMY

according to circumstances as a buyer or seller of eitber. But
tbe discussion of that case was simplified in otber respects by
using tbe more limited conception of demand.

For every conceivable system of prices# in accordance with
tbe law of marginal utility, each person in tbe market will have
a certain demand for each commodity ; indicating either that be
wishes to acquire, or if be possesses it already, to retain, a particular
quantity. If bis total utility function is expressed, as before,
by F{x, y, . •)> equations, already set forth

on page 49 : —

F'x :F'y: F'si , . . = : pc : . . . and

altogether n equations in which all the letters have the same
meaning as before except that the commodity prices Pa, p^i etc.,
are no longer to be regarded as given, but as unknown quantities.
These prices may also be regarded as expressed in terms of one
particular commodity selected as a unit of value : in which case
pa i^^j) is constant (= 1), or else in terms of a measure of value,
such as money, which takes no part in tbe real exchange. In
both cases, if tbe form of tbe function F{ ) is assumed to be
known, all tbe n unknown quantities of goods x, y, 2 , etc., can be
obtained from this system of equations ; if one of tbe commodities
is itself the standard of value, the quantities are expressed in
terms of the w — 1 prices of tbe remaining commodities, still
unknown for the present ; otherwise they are expressed in tbe
n — 1 ratios between the money prices of tbe n commodities.
For each person in the market there is an analogous system of n
equations, from which the quantities of all goods demanded may
be expressed in terms of the n — 1 relative prices of the
commodities.

We have now to describe the position of equilibrium, where
the sum of all the demands for the commodity {A) must equal
the total quantity in the market. A, and the same as regards
(B), etc. Thus, if we treat each of the parties to an exchange in
the same way, and mark them out by the suffixes 1, 2, 3, etc.
(xj, X 2 , a ?3 . . . etc.), which for precision we ought to

have used before, we obtain the equations : —

S{x) = A, Z(y) = B, U(z) = C . . .

in which 2J{x) stands for tri + £C 2 + ^3 + • *

The number of these equations is n ; but only n — 1 of them
are really independent ; one of them can always be derived from

THEORY OF VALtJE 67

tlie otliers by means of the equations already set out. Thiss if
we add together the equations (on p. 66),

+ + -f . . . =^Pa-<^'TPb‘^^!Pc,C~r - • •

and all the corresponding equations relating to the other persons
in the market, we shall obtain : —

-j- pc-£z + . . .^p^.A p^.B -f + • • •

And smce this equation could also have been found by the addition
of the corresponding members of the equations Uix) =
2{y) = B, etc., after multiplying each of them by p^, etc.,
the above assertion becomes obvious. It is also deducible a priori,
for if goods are only exchanged for goods (so that money, if it is
used at all, functions in a merely formal manner} then, if the
demands for all the commodities with one exception are equal
to the existing supplies, the same must apply to the last com-
modity (what the holders do not wish to retain has, of course,
already found purchasers). But these n — 1 equations are
sufficient for the solution of the problem, for all the quantities
involved — t/i, etc. — can, as has been shown,

be expressed in terms of the n — 1 relative prices of the com-
modities, so that finally we shall have as many equations as
unknowns. Thus the problem is perfectly determinate.

If, on the other hand, we had imposed the further condition
that the exchange must only take place directly, in other words,
that the quantity of commodity {B) which is demanded by the
holder of (A) should pay in full for the quantity of (A) demanded
by the holder of ( B), then the problem would have given us more
independent equations than unknowns and would thus have be-
come over-determined ; unless at the same time we had foregone
the demand for correlation between the commodity prices, in
which case the possible exchange ratios between n goods would
be not n — 1 only, but (n — 1), i.e. for three commodities 3,
for four 6, etc.

In any case, by the method we have followed, we can only
arrive at the relative exchange values of the goods or their
relative prices — ^not at their actual money prices, which must
remain quite undetermined ; this is obvious so long as we regard
the functions of money as purely formal. If, after the exchange
is over, all the money employed has returned to the hands of
its first owner, it is a matter of complete indifference to him,
as to everybody else, whether in the actual exchange transaction.

68 IJECTXmES ON POLITICAL ECONOMY

one unit of goods was exchanged for more or less units of money ;
in other words, whether, in order to effect the transaction, the
money circulated a greater or lesser number of times among
the parties in the market before it ultimately returned to its
starting-point. In reality, of course, this is never a matter
of complete indifference. In every market, there are persons
for whom money is something more than this ; who exchange
goods for money or money for goods in order to obtain at a later
date new goods for the money they have acquired. To them,
clearly, the exchange value of money— and especially its
fluctuations — ^are by no means unimportant ; and the function
of money in any particular market transaction becomes, in
actuality, not merely formal but also real. In other words,
money prices, as such, have their laws and their conditions of
equilibrium ; but we cannot develop them here because they are
very closely connected not only with the nature of money as
a commodity and with the conditions of its production, etc.,
but also with the time-element whose importance in human
economy we have not yet considered — ^in other words, with the
theory of capital and interest.

4. Objections against the Theory of Marginal Utility.

Exceptions to the Theory

The objections which were made in various quarters against
the theory of marginal utihty when it was first propounded,
were largely due to a misunderstanding of its real meaning and
may, for that reason, be ignored. In the main, they were based
on the fact that its advocates held too one-sided a view of the
continuity of economic quantities, of the simplicity and flexibility
of the economic system, etc. ; on the other hand, the critics
exa^erated the discontinuity of the quantities and the
complexity of their interaction, and also exaggerated the power
of ecoTiomic friction. That, in fact, discontinuity occurs at many
points, and must occur, scarcely any adherent of the theory of
marginal utility has denied ; it exists, after a fashion, whenever
the price of a commodity is so high that some buyers cease to
purchase it or some sellers dispose of the whole of their stocks ;
or when the price is so low that some sellers will not dispose of
any of their stocks, whilst not yet appearing as purchasers, etc.

THEORY OF VALrE

69

In sucii circumstances, of coiirse, marginal utility has ceased to
regulate the quantities of goods demanded or supplied by sueii
persons. Yet the mathematical treatment of the problem raises
no difficulties, for these quantities now enter into the equations
as constants. A still more obvious case of discontinuity arises
when the commodity which is the object of exchange only occurs
in large indivisible units — such as houses, ships, etc. In some of
these cases, the determination of a market price in the ordinary
sense is impossible, and business is reduced more or less to
isolated exchange, in Vvhich, as we have seen, the price is, from
the point of view of abstract theory, indeterminate. In others
of them, as in Bohm-Bawerk's often-quoted example of a horse
market (cf. Positive Theory of Capital, pp. 203-13), an
equilibrium price will be reached, at any rate approximately,
which will be determined by the marginal pair of buyers and
sellers. But it is only for these that the marginal utility (which
in this case is roughly equal to the total utility) will correspond
with the price. All other buyers and sellers will acquire the
commodity at a price more or less below — or sell at a price
above — ^its utility to the person in question.

In reality, however, there is one circumstance which, even
in these cases, imparts to the law of marginal utility a wider and
more individual application than one would at first sight suppose,
namely, that most goods on the market are supplied in a number
of different qualities. At a horse fair, for example, there is
usually not merely one kind of horse, but horses of the most
varied kinds as regards age, strength, swiftness, endurance, etc.
For example, suppose a buyer has to choose between three horses,
at 500, 550, and 575 shillings. At these prices he may prefer the
second horse to both the cheaper and the dearer one : in other
words he values the difference in quality between the first
and the second at rrwre than 505., but that between the second
and third at less than 25s. If every conceivable price and
quality were to be found in the market, every buyer would
certainly extend his demand up to the point at which a further
addition in quality would exactly correspond to the additional
price asked. If we conceive this diSerence of quahty (looked
at subjectively) as being the marginal utility of the commodity
horse ’’ (which would be in full accordance with the genesis
of the concept) then, here also, the marginal utility, at least for

70 LECTURES ON POLITICAL ECONOMY

buyers, would be approximately the same as the price or, at
any rate, proportional to it. (Something similar also applies
to selers if they deal in horses on a large scale, so that each
of them has several horses to sell.) On the other hand, the
tcOal utility will not, as is usually the case, stand in any definite
relation to it. For the horse which the buyer now considers
too dear at 575s, he would gladly pay 6-700^., perhaps
1,(K)0 if it were the only one in the market and he had to
have a horse. And the same applies to a number of similar cases.

On the other hand, it often happens, even in the case of
goods which are physically perfectly divisible, that individual
consumption is not expanded or contracted by every change in
price. A very important case is the consumption of necessities.
Adam Smith remarked that the human need for food is limited
by the size of the stomach, and subsequent investigations
have shown that a person under given conditions, doing
ordinary manual work, consumes almost constant quantities
of the principal foodstuffs — ^namely, about 120 gr. of
albumen, bO-fiO gr. of fat, and about 500 gr. of carbohy-
drates. With exhausting work (e.g. soldiers on the march,
etc.) more is consumed, especially more fat. Any material
reduction of these quantities would produce the most serious
consequences ^ and would sooner or later render the person
in question unable to carry on his work. An excess^ on the
other hand, has no value at all and would, in the long run, cause
sickness and discomfort instead of added strength and well
being. Here, evidently, is a case in which consumption essentially
Vicks elasticity ; or, what comes to the same thing, in which the
total utility and the marginal utility are themselves discontinuous
quantities, so that the latter falls rapidly, from a very high
value to zero, or even becomes negative. If each of the
three foodstuffs were only found separately in one kind of
commodity, then, no doubt, there would be striking peculiarities
in the price-formation of articles of food. In reality, all three
are to be found, though in different proportions, in most edible
commodities, and in addition, as everybody knows, even the com-
monest foodstuffs exist in different qualities, according to the

^ To what extent more recent investigations concerning the possibility
of substituting carbohydrates for albumen may change the above view, I shall
not discuss here.

THEORY OF VALUE

71

degree of digestibility, taste, perishability, etc. Hence there is
room for the law of marginal utility to operate in individual
consumption. Moreover, as we have already pointed out,
foodstuffs not only serve directly as human nourishment, but
also have indirect uses — especially as fodder for animals, etc.

Two objections mentioned above are of greater weight.- It
is only too true that concrete economic phenomena are infinitely
too complex to be adequately explained by any theory —
including the theory of marginal utility ; for, in addition to
purely economic forces, such as the quest for the greatest possible
personal gain, there are others of a different kind : mutual
goodwill, general philanthropy, social considerations, etc., which
nearly always play some part. As a first approximation, however,
we are justified, as we have said, in ignoring ail other factors.
It is by no means certain that, with the adoption of the principle
of marginal utility, even (for example) the altruistic elements
in social life would not also permit of analogous treatment, to
the extent to which they must be regarded as relevant to the
question of price-formation. The attempts made by recent
writers to give a rational account of the theory of public finance
seem to show that this is really the case.

On the other hand, what is called economic friction
{caused hy habit and inertia) so far as its effects extend — ^and
they are very significant — constitutes an exception to our
conclusions. It is indeed true that habit is, with most of us,
the fruit of economic observation or instinct. It arises because,
under given conditions, it proves the best means of achieving
a desired end ; but these conditions often originate in the remote
past and have, perhaps, now given way to something quite
different. During periods of great material progress all institutions
based on custom may, therefore, easily appear as anomalies
and even as non-economic phenomena, injurious both to the
individual and to society, and yet persisting. The Italian
economist, Pareto, in his earlier work, Cours d'Economie politique
(voL ii, p. 9 et seq^ and p. 281 et seq,) gives an interesting,
though somewhat incomplete, theoretical analysis of economic
friction — or, more correctly, of economic inertia, which plays
much the same part in relation to other economic forces as does
the so-caUed principle of inertia in mechanics.

But the most important objection to the theory we have so

72 LE(irUKES ON POLITICAL ECONOMY

far developed is no doubt the fact that our assumption oifree
competition is, and can be, only incompletely realized in actual
life. The field in which it particularly prevails is, as everybody
knows, that of wholesale trade ; but consumers and owners of
goods do not then, as we have assumed, come into direct contact
with each other, and consequently the interests of consumers
in price formation only become effective at a later stage, and are
not direct. On the other hand, in the field in which consumers
appear directly (i.e. in retail trade) the law of free competition
only operates with certain limitations. Still more stri kin g
exceptions are afforded, of course, by industrial monopolies in
the narrow sense.

Before we pass on to a more detailed consideration of these
exceptions, some of which are of the greatest interest, we shall
consider a question, the real significance of which can only be
understood after detailed inquiry in the social section of our
work, but which, even from a purely theoretical point of view,
is of such importance that it cannot be entirely ignored at this
point. I refer to the question of the economic advantages of free
exchange or of free competition in general — a question which
is beloved of writers on the theory of value, but of which,
unfortunately, not very much has actually been made.

5. The Gain from Free Exchmge

It is a corollary of the economic principle which underlies
all our studies, that we only exchange for the purpose of gain
and, under given conditions, we always endeavour to exchange in
such a manner, and in such quantities or proportions, as will
yield the greatest possible gam. The doctrine that marginal
utility is proportional to price ; that the subjective utility of
the last unit acquired is equal to that of the last unit disposed
of ; and that the increase in utility at the margin of exchange
is zero, are all different ways of expressing this postulate, and
closely correspond with the criterion which pdicates a maximum
or minimum value in mathematics. It is easy — ^though it would
involve a serious confusion of ideas — ^to cite this as a proof that
free exchange brings a maximum satisfaction of needs to all
participators ; that is to say, as great a measure of satisfaction
as is generally consistent with the prevailing conditions of

THEORY OF VALUE

73

property or ownership — ^from which, of course, we must proceed
in a theoretical consideration of price-formation. As we know,
it was not the advocates of the theory of marginal utility who
jBrst advanced this view. It is rather the fundamental
principle and dogma of free-traders — ^the physiocrats and their
descendants of the so-called Manchester school — ^both in the
field of production and of trade proper. The well-known
saying, laissez-faire^ laissez-passer ” — actually “ laissez worn
faire'^ (^‘let us manufacture our producte freely and without
restraint’’) and ^^laissez passer Us rmrchandises^^ {“let our
goods freely pass the boundaries of the province or the
state ”), which epitomized the principles of industrial liberty
and free trade — ^became, as we know, the motto of this school,
which was guided by precisely the above argument. If any-
body may freely dispose of his po^^ions and Ms productive
powers, he will undoubtedly seek to make the best possible use
of them ; it was assumed, therefore, that both the individual
and society will be guaranteed the greatest possible advantage —
always, of course, with the very important qualification : so far
as existing proprietary rights permit. The harmony economists,
who endeavoured to extend the doctrine so that it might become
a defence of the existing distribution of wealth (itBelf a product
of free competition and consequently the best possible dis-
tribution), cannot, in this respect, be regarded as representative
of the views of the physiocrats and the classical free trade school.

Although the propounders of the theory of marginal utility
were certainly not responsible for this all-too-optimistic view
of the advantages of free trade, yet some of them cannot be
entirely absolved from the charge of having helped to maintain
faith in it by their support, and their apparently logical proof,
of its doctrine. This is especially true of Leon Walras and his
immediate disciples. Walras himself relates ^ that, in his youth,
he was once helpless in the fece of an onslaught on
the foundations of free trade theory made by the Saint
Simonist, Lambert Bey, who maintained that the exchange
values arising from free competition were neither the only ones,
nor the best. Walras realized that the theory, if it was to be
maintained at all (wMch he Mmself never seems to have doubted),
must be proved more satisfactorily than had Mtherto been
^ J^tvdea d'economie pohtique p. 466.

74

LICTUEES ON POLITICAL ECONOMY

done. n fandxait prouver que la libre concurrence procure le
TTiainTmim d’utilite.” And this view was in fact the starting-point
of Lis own work in economics. It is almost tragic, however,
that Walras, who was usually so acute and clear-headed,
imagined that he had found the rigorous proof, which he missed
in the contemporary defenders of the free trade dogma, merely
because he clothed in a mathematical formula the very arguments
which he considered insufficient when they were expressed in
ordinary language.

In the following words — ^which he italicizes — ^Walras sums
up his investigations into free exchange, especially exchange of
two commodities : Exchange of two articles in a market where
jfree competition prevails is an operation by which all holders
of either of these two articles, or of both, can obtain — ^in the
first edition he wrote only obtain ” and not can obtain ’’ —
‘‘ the greatest possible satisfaction of their needs consistent
with the condition that they must dispose of the goods they
sell, and accept those that they buy, in one and the same
proportion for all Although it is possible that this somewhat
vague formulation may be interpreted in a way which can be
defended, yet in fact both Walras and his disciple and successor,
Pareto (in his earlier work already quoted employ it precisely
in the sense that, under free competition, and under the existing
laws of property, each of the exchanging parties obtains the
maximum amount of satisfaction for his needs, with any system
of uniform prices in the market. The latter condition must, of
course, not be forgotten. The objection which has sometimes
been made to this theory — namely that if free competition
produced the maximum satisfaction of needs, it would be
impossible to increase the available sum of this satisfaction
hy gifts — does not, at least in Walras’ opinion, afiect the essence
of the argument. The ‘‘ exchange conditions ” which prevail
in the case of gifts, where one party receives no material
compensation, could not in general prevail in the market — ^not

^<X’echange de deux marchandises entre elles sur un marche r6gi par la
libre concurrence est une operation par laquelle tous les porteurs, soit de I’une
des deux marohandises, soit de Tautre, soit de toutes les deux, peuvent obtenir
(obtiennent) la plus grande satisfaction de leurs besoins compatible avec cette
condition ^ de donner de la marcbandise qu’ils vendent et de recevoir de la
n^cbandise qu’ils ach^tent dans une proportion commune et identique.
{EUmeruts d^economie polUique pure, 4me ed. lOme Le 90 n.)

® Concerning his later views on this question, cf. pp, 82-83,

THEORY OF VALUE

75

even by the strictest orders of the authorities ; for the holders
of the goods for which only thanks would be received in payment
would, as a rule, prefer to retain them for themselves.

Nevertheless, Walras’ theory, as generally understood, and
even as applied by himself, is undoubtedly wrong ; and it is the
more incomprehensible that he should have propounded it, since
he hi mself had proved a few pages earlier that, in the exchange
of two commodities, many equilibrium positions are possible.
In the sense in which the word is here used, all of these cannot
simultaneously represent positions of maximum satisfaction.
What distinguishes prices fixed by free competition from all
other prices, the thing which finds a mathematical expression
in Walras’ formulae, is simply and solely this : that, under
competition, each of the exchanging parties can and does go
on exchanging up to the point of what we have called rdMive
satiety — ^relative, that is, to the existing system of prices — so
that at those prices none of them wishes to exchange any more.
But this cannot be the case where, for example, by decree of the
authorities, some other uniform price system is established in the
market — ^which was formerly very common. There will then
always be persons who, on ceasing to exchange, have not yet
reached the point of satiety, though at these prices they would
gladly exchange more of their own goods for a corresponding
amount of other goods, if only these could be obtained at the
established price ; and what is more — ^they might even be
inclined to lower the price of their own commodity or to offer
higher prices for the commodities they desire, if this were not
forbidden by the authorities. Further reflection shows that this
must occur to all those who are so favoured by the oflBlcial
regulation that they obtain a higher price than they would have
obtained under free competition. On the other hand, those who
are handicapped by the prescribed prices, in so far as they might
have obtained better prices under free competition, will continue
to exchange to the point of satiety. However, if the owners
of goods who are favoured by the prescribed prices are obliged
to discontinue selling their goods sooner than they would wish,
because they can no longer find purchasers, there is nothing to
prevent them receiving in payment a larger quantity of other
goods than they would have received under free competition,
even though, under competition, they would have found

76

LECTUEES ON POLITICAL ECONOMY

purchasers for a larger quantity of goods. In this case it is
clear that their gain from the exchange — even though it may
be unequally distributed, so that some of them get very little
whilst others are able to satisfy their needs fully — ^would, on
the whole, be greater, perhaps much greater, than under free
competition. Moreover, this is a fact which scarcely anyone who
has considered the matter wiU doubt. For a high price iSxed by
authorify has, in this case, the same effect as a general agreement
between sellers not to go below a certain price, and there is no
doubt that such an agreement, if it is loyally adhered to, and the
profit divided among the sellers with any degree of uniformity,
may, at least at first, be of great advantage to them.

Walras (and Pareto), if we take them literally, thus go further
than the free traders themselves, for the latter have not denied
that a restriction of free competition might be most advantageous
to a small privileged minority. On the other hand, the classical
free trade school regarded it as self-evident that the loss in such
cases would be much greater than the gain ; in other words,
that the great mass of the population would always suffer by
measures of this kind, and that consequently they could only
benefit a relatively small number.

In this form, the principles of the free traders often gain
acceptance even by those who, in practice and policy, are their
opponents. In principle,’’ in theory,” in the abstract,” and
so on, these doctrines are regarded as indisputable. Objections
are made — ostensibly at any rate — only on ‘‘ practical ” grounds,
which economic theory does not take into consideration ” : the
beneficial effects of protection on “ infant industries ”, the
necessity for a country to be self-supporting in case of war,
and so on.

Nevertheless, however plausible it may appear, the doctrine
of maximum gain under free exchange cannot in strict theory
be defended even in this form. In reality there are, as people
are now generally beginning to realize, several important
exceptions. In the first place, it is clear that if we are to compare
the advantages or disadvantages to different persons in order
to obtain from their algebraic sum what is called the economic
gain or loss of a certain mode of action, then the basis of
comparison must be determined. If there is no such basis, or if
it is incapable of exact formulation, then it is impossible to

THEORY OF VALUE

77

determine whether a particular economic distribution is
advantageous or otherwise. That a purelj external equality
cannot in all cases be satisfactory is evident. If, for example,
we were to deprive a violin virtuoso of his instrument, a genuine
Stradivarius, in order to give it to somebody else who could only
use it as fuel, it is clear that the economic gain and loss, however
high we might rate the need of the latter for fuel, could scarcely
be equal. Broadly speaking, however, we can make an abstraction
from individual diSerences and assume that, m their capacity
for enjoying the good things of life and in the strength of their
desires, men are by nature the same. On the other hand, rhere
is one inequality from which we can never abstract, without
making a serious mistake, namely social differences and the
unequal distribution of property. If we assume that the rich
man carries his consumption so far that the marginal utility,
the utility of the last unit, is little or nothing to him, whilst on
the other hand, the poor man must discontinue his consumption
of practically all commodities at a point at which they possess for
him a high marginal utility, then it is not difficult to imagine,
as Bohm-Bawerk remarked in his Grundzilge (attacking Schaffle),
that an exchange between a rich man and a poor man may
lead to a much greater total utility for both together — and
therefore for society as a whole — if it is effected at a suitable
price fixed by society, than if everything is left to the haphazard
working of free competition. And what is here true on a small
scale is just as true on a large scale. Thus, for example, the
fixing by society, or by a union of workers, of a minimum wage
or a maximum working day would, within certain hmits (which
may sometimes be very narrow), be of distinct advantage to the
workers and consequently to the most numerous class of society.
The same effect might be obtained, especially in undeveloped
countries, by a system of tariffs if it prevented too pronounced
a flow of labourers to agriculture and a consequent increase of
rent at the expense of wages. Broadly speaking, there is
a contradiction in categorically denying this possibility, whilst
on the other hand admitting that a changed distribution of
'property might be to the advantage of the most numerous class
in society. For, in reality, property only exists for the sake of
the advantages, or income, which it yields ; if these are changed
by influencing commodity prices, then an attack has really been

78

IJICTURES ON POLITICAL ECONOMY

made on the distribution of property, or at any rate on tbe effects
of tHs distribution.

Tbe theoretical aspect of this somewhat difficult problem will
be made clearer if we begin by taking a concrete example ; for
which purpose we will select the commodity “ labour and its
corresponding price “wages”. We assume that the supply,
demand, and price of labour have hitherto been determined by
free competition, and that the average working day has been
fixed at 10 hours and the average wage at 1$, 8d, per hour. Even
if this equilibrium position were the only one and therefore
necessarily stable, so that a fortuitous rise in wages would cause
the supply of labour to exceed the demand, and so on, we may
assume that the workers by means of their organizations, or the
help of legislation, succeed in forcing a reduction of working
hours by haK an hour to hours per day. This will inevitably
have the same effect on the market as a diminished supply of
labour,^ and will result in a rise in wages per hour. If time-wages
rise more rapidly than working hours are shortened, for example
l\d. 2d. or (which is conceivable, though not very probable),
then it is clear that the workers would reap a distinct advantage
from the change. If, on the other hand, the rise in wages stopped
at Id., or even ^d. per hour, it might at first sight be thought
that the workers would lose by the change — for their daily wages
would fall to 16s. 7Jd. or 16s. 3d. instead of 16s. 8d. Here it should
be remarked, however, that if the original working day, as we
suppose, was established under free competition, then the labour
and inconvenience of the last half-hour must have approximately
corresponded to the wages offered for it, i.e. lOd. If not, it is
difficult to see why, at that wage, the worker did not voluntarily
prolong his working day. We may, therefore, assume that the
half-hour of leisure gained for the worker has a value of about
lOd. (in any case it has at least the money- value which the
worker, by virtue of reduced muscular exertion, saves on his
daily expenses). The slight reduction in his daily wages is there-
fore more than compensated by the increase of leisure time ; in
other words, the increase in wages of 9^., or 4Jd. respectively
which the worker now obtains for his 9j hours* work per day is
to be regarded for him as a pure net gam.

As may be seen, this reasoning is general. There is no doubt
that sellers of any commodity whatever can, by common agree-
ment, obtain an economic advantage ; but it should be noted

• ^ is only our intention here to illustrate a theoretical principle, we

Ignore the otherwise important circumstance that shorter hours of labour

usually give rise to a greater or less increase in the efficiency of labour.

THEORY OF VALUE

79

that we can only definitiely assert this on the two assumptions
we have made : that the previous price relations are determined
under free competition, and that the new price or supply does not
vary too much from the old. Otherwise, we cannot always
assume that the quantity of goods (in this case increased leisure)
which the seller himself retains as a result of a decreased supply
(or in consequence of higher prices, if this was a primary cause)
has for him even approximately the same value as their price.

On the other hand, to what extent this undoubted gain for
one class of society is a gain for society as a whole naturally
depends upon whether it is greater than the loss which falls upon
other classes of society — this case primarily the employers,
and through them the consumers : and, in the last resort, the
other factors of production : land and capital. For them also
marginal utility and price are equal under free competition, and
their net loss is therefore simply the higher price which they
must now pay for the labour which they demand. They lose, in
other words, exactly as much in exchange value as the workers
gain, and the only question is whether a penny or two nhore per
day in the hands of the workers is of greater advantage than a
penny or two in those of the propertied classes — 2u question which
must certainly be answered in the negative, if we are to maintain
the dogma of the unqualified social utility of free competition.
The further objection which might be made, that a decreased
profit in the hands of employers would lead to a decrease in capital
accumulation, and would thereby indirectly injure the workers,
will be examined at a later stage.

Treated generally, in algebraic form, the problem presents
itself in the following manner. Let y) be the total utility
which one of the parties to the exchange, who originally possessed
the quantity b of the commodity {B) can count upon after a
completed exchange ; it is expressed as a function of the quantity
acquired, x, of the commodity {A) and of the quantity y of (B)
disposed of ; or respectively of the quantity (h — y) of the com-
modity (B) retained. The price p of the latter commodity we
suppose to be expressed in terms of (A), so that x = p.y,

A slight change, Ap in the price p would thus produce the
corresponding changes Ax and Ay m the quantities x and y
exchanged, these being connected by the relation Ax^y.Ap
+ p. Ay m which A x and A y evidently have opposite signs. As an
expression of the change which the total utility undergoes we
obtain

A4, = + ^Ay = f^i^Ay + yAp) + f^Ay.

80

LECTUEES ON POLITICAL ECONOMY

But in consequence of the fundamental condition of free exchange
we obtain : —

. 3 ^

3(6 — y)

in which ^ is, of course, a function which diminishes with respect
to y. The above formula may therefore be simplified to

dy

U

A<l> = ^.y.Ap

wMci indicates that, with a sujfficientlj small change in price,
the seller obtains practically the whole of the increase in price
(of his own commodity) as a net gain.^ If we now add the
analogous expressions for all parties to the exchange and count
the quantities of (A) sold (and consequently the quantities of
(B) acquired) as negative^ we obtain

in which by the summation sign we understand a summation of
the bracketed expression for each of the indices 1, 2, 3, etc., so

that the ^ with the appropriate index indicates the marginal

utihty of (A) after exchange to each of the exchanging parties
taken m order. The sum in question is evidently independent of A p
and in general is not equal to zero. As we can give Ap either a
positive or a negative value, the whole expression can always
be made positive — which proves that in normal cases there can
always be found a system of uniform prices at which exchanges
will produce a larger sum of utility than at competitive prices.

If, on the other hand, after exchange is completed, the
marginal utility of one commodity (and consequently also of the
other) were the same for all the parties to the exchange, then
the above expression can be reduced to

and this is always zero, since Bg, the algebraic sum of the total
quantities of the commodity (B) disposed of or acquired by the

^ y is the quantity of his own commodity (B) which he originally sells ;
y.ApJs consequently the additional quantity of the commodity {A) which he
would obtain as a result of the increase in price if he could continue to sell

the same quantity y of his own commodity ; is the marginal utility of (A)
and hence .y.Ap is the gain in utility derived from the increase in (^).

THEOEY OF VALUE

81

parties to tlie exchange, mnst be equal to nothing. This condition
of equal marginal utilities implies — ^approximately, but not exactly
— a position of economic equality between persons ; and in that
case — ^though not otherwise — ^free competition would secure a
maximum satisfaction to all parties to the exchange.^

There is no need to emphasize the fact that an encroachment
on free competition, if it is to yield the above result, must be
effected in the right direction. Unrestricted liberty is in general
infinitely to be preferred to a misguided system of restriction
and compulsion. In so far as the government of a country is

^ As an example of how even an experienced mathematician may be led
to erroneous conclusions in this field, we may mention the argument of
JjBxiiih&Tdt (IlathemcUtsch^ BegriinduTig der VolksmTtschaftsIehr&). He assumes
two parties to an exchange, one of whom from the begmnmg possesses a units
of the commodity (A) and the other b umts of the commodity (B) and, for
the sake of simplicity, he supposes the total utility derived by each person
from the commodity (A) to be expressed by the same function, /( ) ; and

similarly ) for the commodity (B), If they then exchange the quantities
a; and y the total utility received after exchange by both parties together is
expressed by iV — S{a — x) (j> (y) -f f(x) -j- ^{b — y). In order that this
expression should be a maximum we must have : —

[_/'(a _ a:) +f'(x)']4x + - ^'(6 - y)']Ay -0 (1)

But in equilibrium we haTe
/'(o - x)

— y)
/'(a;)

= ?.

also

Ax

where p is the price of (B) in terms of (A). Thus the above equation is satisfied,
and consequmtly Launhardt concludes, the equilibnum price determined by
JEree competition is tbe one which, among all uniform pnees, produces the
greatest ^ditional utility for the two (or for all) parties to the exchange.

The proof is evidently false. If we desired to discover the absolute
maximum of N we should have made x and y independent and would then
have obtained

f'(x) =f'{a - x) and ^'(y) = ^'(6 - y)

These equations are clearly sq,tisfied by the values x — y = in other

words, the parties should simply exchange half their stocks. Smee this result
is not generally consistent with exchange at a uniform price (and is perhaps
outside the possibilities of free exchange) we must impose the condition that
one of the parties (the one who is at a disadvantage in regard to price) continues
to exchange to the point of satiety. We thus obtain the equation

y ^ f'{a — x)

By differentiation of this equation and elimination of Ax and Ay with the
help of (1) we obtam, according to circumstances, a maximum or a minimum
of N, but in neither case an exchange at an eqmlibrinm price.

By way of further proof, Launhardt tries to show, by means of an
arithmetical example, that a price which would produce the greatest possible
gain for either of the parties would, nevertheless, yield to them both a smaller
surplus utility than would the equilibrium price. But a close examination
will show that this result is due simply to the fact that he has unconsciously
gone beyond the nght maximum.

o

82 LECTUEES ON POLITICAL ECONOMY

based on democratic principles, there is a certain, ttongli not
always reliable, guarantee that such measures will be introduced
only when they are to the advantage of the vast majority ;
whereas when commercial and industrial policy are in the hands
of a privileged minority there is a strong presumption to the
contrary.

It may also be observed that a restriction of free exchange,
of freedom to enter into labour agreements and of the right to
free disposal of property — either by means of government
intervention or by mutual agreement between buyers and sellers,
employers and employees, etc. — ^is nevertheless a retrograde step,
in so far as it usually tends to reduce the sum total of the means
of satisfaction physically attainable — even if, under certain
circumstances, it may lead to a socially more desirable distribution.
We shall return to this important and diflS.cult question at
a later stage (p. 142 seq,).

In a word, free exchange in economics may be compared
to the method of “trusting to nature” in medicine — ^when
the doctor really does nothing, but leaves nature to efEect its
own cure. The term physiocracy means precisely this. In
a state of perfect health, which corresponds to a system of
economic equality, this is certainly the only correct treatment.
Even in ill-health it certainly has a great advantage over bad
treatment and dubious medicines. On the other hand, it cannot
compare with a really scientific treatment which assists nature
in a reasonable manner. And, in the last resort, the efiects of
even the most brilliant cure cannot be compared with those of
rational hygiene, which aims at preventing disease and preserving
health The application of the first part of the s imil e should be
clear from what has been said ; the latter will be elucidated
when we come to deal with the social section of political economy.

In his last work, the Manuel d^economie politique, as well as
in various earlier essays in the Giornah degli Economisti, Pareto
returned to a detailed consideration of the problem of the
“maximum d’ophehmite ”, as he calls it, which would result from
free competition. He defines this maximum as the point or
position, from which it is impossible to move while ensuring a
gain in utility or ophelimite for all participators in the market.

With such a definition it is almost self-evident that this
so-called maximum obtains under free competition, because if,

THEORY OF YAlT

after an exchange is ejected, it were possible bp rieans of a
forther senes of direct or indirect excbanges to produce an
additional satisfaction of needs for the participators, then to that
extent snch a continned exchange woidd doubtless take place,
and the original position conid not be one of dnal equ^nbrinm.
The same would also be true of production. As scon as a cbange
in production is more profitable both for producers and for tneir
customers — or, from one point of view, for aV: o^ers of "-be
means of production, workers, landowners and capitalists — tnen
it is difficult to understand why, assuming genera: mobilitp, it
should not happen. But this is not to say :hat the resoit c:
production and exchange under free ccmpetition will be satis-
factory from a social point of view or will, even approxiinateij,
produce the greatest possible social advantage.

Hence, even m this new guise, Paretc s dcctrinc eontribnces
nothing. And — what is worse — ^it tends to cbbcore the fact,
which we have already pointed out and which we shah dev^elop,
that social prediction under free competition {with certain
reservations) does really lead to a maximization, in the usual
and proper sense, of the means of satisfwng human wants. In
this respect, therefore, and of course disregarding the distribu-
tion of the product, it achieves as much, or almost as much, as
we can imagine under rationally organized production in a
collectivist society.

6. Pricing under Imferjed Competiiian
A. Joint Supply arvd Joint Demand

We must now give an account of the principal cases in
which perfect competition between the holders of a particular
commodity does not exist, either because of natural circumstances
or legislative regulation ; and of the effect on pricing of such
restrictions. We may begin with the case already mentioned,
in which two commodities are bound together, either on the
demand side (where the consumption of a certain quantity of
one is a necessary condition for the consumption of a certain
quantity of the other) ; or on the supply side (where the technical
conditions of production are such that the one must always
be produced simultaneously with the other in more or less
definite proportions). The former, which Marshall called joint
demand, may, however, without difficulty be treated as a special

84 LECTURES ON POLITICAL ECONOMY

C£U3e of tie laws goveiming market prices wHcl we lave already
formulated ; and may, tlerefore, be passed over. Well-known
examples of sucl a demand occur in tie case of commodities
dependent on eacl otler eitler in consumption or individual
production, sucl as nails and wire ; knives and forks ; lamps,
wick, and oil ; ink, pens, and paper, etc. Because of tlis relation,
the consumption of ink depends in a mud higher degree on the
price of writing paper and postage than on the actual price of
ink — and so on. Actually, as we lave already observed, nearly
all demand is joint in the sense that different commodities affect
eacl otler and are tlerefore, to some extent, mutually conditioned.
That they should be demanded in absolutely fixed proportions
may be regarded as a special case, which is of minor importance.

The second group of phenomena, which has been called
(also by Marshall) joint supply, really belongs to the theory of
production, and the regulation of exchange values under the
influence of production, which we have still to describe. But
it seems to be desirable to touch upon this question here
because the related phenomena have been taken by some
economists as a pretext for an attack on the whole classical
theory of exchange — ^not so much with the object of criticiziug
it in the manner we have done in the preceding pages, but of
replacing it by a very peculiar theory of pricing, which has
never been very clearly formulated. Thus, the series of supposedly
new price categories, which F. Neumann set up in his articles
on value and price, in Schonberg’s Handbuch, are really nothing
but various examples of joint supply. If, before the advent of
lifts, town flats commanded a lower price the higher up they
were, then according to Neumann this would constitute an
exception to the principle that prices must correspond to costs
of production. Costs of production, he says, are higher for the
upper storeys since, in building them, the material must be
carried to a greater height, and the weight of these storeys
renders it necessary to make the supporting walls thicker than
would otherwise be the case. But the obvious explanation is
that, in addition to floors, walls, and ceiliug, a house must have
land on which to stand and a roof to cover it — of which the
former, particularly, is usually very expensive to buy (or, as in
England, to lease). These costs, or the interest on them, must
be distributed over the rent of all the flats and it is not possible

THEORY OF TALUE

85

to determine a jmori by wliat principle this should be done.
As we have already indicated in an analogous case, the rent of
the different flats is simply regulated by demand, that is to say,
mainly by their respective comfort and suitability for various
purposes ; or, in the last resort, by their marginal utility. Ail
that really matters is that the total rent should be sufficient to
pay interest on all the costs of building, including the cost of
the site. The high cost of building sites in towns has led, as is
well known, to the erection in recent times of lofty steel and glass
structures on the model of the American skyscrapers ; otherwise
all buildings would presumably be erected only one or at most
two storeys high — as in country districts. It is the same with
all other examples adduced by Neumann. As an example of
joint price ”, he describes how the shares in the cost, which
are borne by the participants in a common drainage scheme, are
not proportional to the actual cost of cutting the ditch through
their respective plots of land. This is true enough up to a point,
but it is entirely due to the fact that the latter costs cannot
be ascertained or imputed, for the ditch might have had exactly
the same length, breadth, and depth, whether one or more of
the interested parties had participated in the enterprise or not.
If, on the other hand, the individual costs can be ascertained —
if, for example, in order to satisfy the wishes of some particular
landowner, it is necessary to follow an otherwise unnecessarily
circuitous route in the construction of the ditch, or if the
enterprise is involved in other special costs which would not
otherwise have arisen — then it is clear that these would usually
have to be defrayed by those who cause them. Usually, however,
such an imputation of costs is impossible, and in that case there
is no other way out than to see that the total costs of construction
correspond to the total contributions and to distribute the latter
equitably. The generally accepted principle (for example, that
of the Swedish Ditching Law of 1879) that each shall contribute
in proportion to the objective utility, i.e. the increase in yield
or rent which the eliterprise brings to him, is by no means the
only conceivable one — or even the best or most reconcilable with
economy and justice. H, for example, one of four interested
parties has gained a capital value of £1,000 and the three
others only £100 each, whilst the total cost of the enterprise
was £500, then the first would gam more than any of the

86

LICTUEES ON POLITIOAIi ECONOMY

others — ^more than aU of them combined — ^if he paid the whole
cost himself and the othem did not contribute a farthing.

In this case — ^unlike the preceding one — ^there is no automatic
economic law of price formation ; for it is really a case of isolated
exchange. Nevertheless the discussion which springs from such
a price-problem is full of interest. An analogous case of the
widest implications is presented in a field which may at first
sight seem far removed, namely, in the theory of equity in
tamiion,

B. Pricing in Beiail Trades

Eetail prices are frequently regarded as exceptions both
to the law of costs and generally to every rational process of
price formation, which is all the more remarkable since these
prices are the only ones which are of direct interest to the
consumer and which are directly influenced by consumption.
Yet the laws of retail prices are perhaps not so difficult to
ascertain and do not seem, in the main, to depend on any other
factors than those which we have already treated, except that
they are more complex and more difficult to unravel. To
a considerable extent, the apparent divergence of retail prices
from the law of costs and from wholesale prices is to be regarded
as an example of the phenomenon of joint supply — ^which we
have just considered. Unlike the wholesaler, whose general
costs for his whole business constitute only a small part of his
annual turnover, the retailer’s general costs for premises, heating,
lighting, advertisement, wages for his assistants and for his own
labour, etc., are very considerable. The first item in particular
assumes large proportions since, for the convenience of his
customers and for purposes of advertisement he must seek
to acquire business premises which are as central as possible.
"What proportion of these general costs shall be apportioned
to each parcel of goods, over and above the purchase or wholesale
price, cannot be determined a priori, but depends upon
a number of variable circumstances. It is of great importance
in this connection that certain kinds of goods require much
more expert hnowledge for their valuation than others ; the latter,
such as sugar, flour, etc., the quality of which anybody can easily
judge, yield, if I am not mistaken, a comparatively small profit.

THEORY OF VALUE

87

With the former goods, on the other hand, the buyer, if he is
not exceptional in possessing such knowledge, will, in order not
to be sold inferior goods, deal with a seller in whom he has
confidence. The service which the retailer thus renders him is
that of an expert buyer, and the customer quit-e reasonably
has to pay him a relatively higher price.

The desire for stable retail prices must also be taken into
account. For many customers it is of great importance to be
able to determine their household expenses well in advance.
Retailers, who usually have a fixed circle of customers, therefore
endeavour to afford this advantage of approximately fixed prices,
which they calculate so that the profit and loss of good and bad
times to some extent cancel out. Naturally, greater and more
permanent variations in wholesale prices are ultimately reflected
in retail prices — ^though, as a rule, later and in a modified form —
just as a thermometer buried deep in the ground responds
slowly to changes of temperature on the surface.^

In conclusion, we should not forget that practically every
retailer possesses, within his immediate circle, what we may call
an actual sales Tnonopoly, even if, as we shall soon see, it is
based only on the ignorance and lack of organization of the
buyers. He cannot, of course, like a true monopolist, raise
prices at will — only in places remote from trade centres can
a considerable local rise in prices occur — ^but if he maintains
the same prices and qualities as his competitors, he can almost
always count upon his immediate neighbourhood for customers.
The result is not infrequently an excess of retailers, apparently
for the convenience, but really to the injury, of the consumers.
If, for example, two shops of the same kind are situated at

^ In an essay in Eicon. Tidskrift^ October, 1908, and also in Ms work,
Dem, ekonomtska fordelningen ock Krisema, Brock Las sought to prove that the
above conception of the relation between retail and wholesale prices is not
correct. Retail pnces, m his view, show a strong tendency to follow wholesale
prices uptoards, but very little tendency to follow them downwards. The
statistics (from America) on wMch Brock bases this assertion would s^m to
show merely that of recent years retail prices have, on the whole, risen as
compared with wholesale prices ; a fact which, owing to the great relative
increase of retailers, is in itself probable and is quite m accordance with what
we are about to say. As a general doctrine. Brock’s view (and that of Lexio
and others) is clearly absurd ; it would imply that retail prices would diverge
more and more from wholesale prices at each cyclical fluctuation which
would lead to absurd consequences. Obviously, we do not attribute any
altruistic motives to retailers when we speak of their endeavour to keep prices
as steady as possible for their customers’ convenience. It is well understood
that it is in the interest of every business man to satisfy his customers.

88 LECTUEES ON POLITICAL ECONOMY

different ends of tlie same street, it would be natural that tbeir
respective markets would meet in tbe middle of tbe street.
Now if a new shop of tbe same kind is opened in tbe middle
of tbe street each of tbe others will, sooner or later, lose some
of its customers to tbe new shop, since tbe people living round
tbe middle of tbe street believe tbat if tbey get tbe same goods
at tbe same price tbey are saving time and trouble by ’mfl.lnng
tbeir purchases at tbe nearest shop. In this, however, tbey are
mistaken, for tbe original shops which have now lost some of
tbeir customers without beiug able to reduce tbeir overhead
expenses to a corresponding degree, will gradually be compelled
to raise tbeir prices — ^and tbe same applies to tbe new competitors
who have been obliged from tbe beginning to content themselves
with a smaller turnover. This should explain tbe observation
which is said to have been made on tbe abolition of tbe octroi
^tbe tax on tbe entry of goods into a town, common on tbe
continent — ^tbat tbe expected reduction in prices never took
place, though tbe number of retailers considerably increased.
Tbe correct remedy, unless one of tbe competitors (such as a great
store) manages to overshadow all the others, is clearly tbe
formation of some form of organization among buyers. But so
long^ as such an association does not exist — and between persons
in different positions in life and without more intimate bonds
it is extremely difficult to establish — ^tbe anomaly must remain
tbat competition may sometimes raise prices instead of always
lowering them, as one would expect.

C. Monopoly Prices

A still more pronounced divergence from tbe formation
of prices under free competition is provided by monopoly prices
pro;^r. Monopoly involves tbe absence of competition, either
absolute ioT a certain class of goods, such as a state jBscal
monopoly (of Uquor, tobacco, salt, etc.), patents of industrial
mventions, etc. ; or only relative, in a dejSnite geographical
area and witbm certain price limits. Every limitation of supply
or of productive power does not necessarffy create a monopoly
—for m that case every price would, strictly speaking, be
a monopoly price, smce none but free goods occur in unbmited
quantities. Tbe ownership of land, for example, is certainly

THEORY OF VALUE

89

the privilege of a more or less limited class, but so long as active
competition exists between landowners, this possession is not
a monopoly and does not lead to monopoly prices for the product
of agriculture, either individual or collective. The diuerence
lies in the fact that a commodity or factor of production, whose
supply is limited, but which is not the subject of a real monopoly,
is offered as a whole at the price it can fetch, or at any rate
up to the point at which the owners themselves prefer to retain
it for their own use. The monopolist, on the other hand,
artificially restricts the available market supplies of the
commodity or factor of production in his possession. His supply
is not regulated by the coincidence of marginal utility and
price. If, indeed, it should happen that he were to offer the
whole of his stock of goods or means of production, up to the
limit determined by this condition, he might nominally have
a monopoly, but the price would not be monopolistically
determined, but would follow the ordinary laws of supply and
demand. His profit would then depend solely upon the natural
scarcity of the commodity. Frequently, however, the monopolist’s
stocks are unlimited — ^as in the case of a patent the use of which
might be extended without special expense tjo all consumers
who would in any way profit by it. But if this is to happen, either
some customers must pay more than others, or there must be
a zero price for all ; i.e. the invention would be on the same
footing as a free good — ^which is actually the case when patent
rights run out. The high price of patented goods is therefore
due exclusively to an artificial restriction of output, as Adam
Smith remarked.

In exceptional cases, as has been said, competitive prices
may prevail under an actual monopoly. Thus the Standard Oil
Company of America, which has absorbed practically all the
petroleum refineries of the U,S.A., fixes its prices, by measuring
the yield of the wells during the preceding days or weeks, at
the level at which consumption is expected exactly to equal
production. Generally speaking, in a case of this kind, it would
often be possible to obtain a larger profit — ^perhaps a much
larger profit — ^if the price were raised, in spite of the fact that
this would reduce consumption. But in that case, the wells
already opened would have to be partially closed down, or
their contents allowed to run to waste — which would presumably

90 LECTDEES ON POLITICAL ECONOMY

cause dissatisfaction among the public, and might lead to the
intervention of the ‘authorities.

If no such considerations exist, it will be to the advantage
of the monopolist to fix his prices so high that he will obtain
the maximum net profit. Every rise in price causes, we may
assume, a falling off in demand. But so long as the falling off
in demand is less than proportionate to the increased profit per
unit of the commodity resulting from the higher price, the total
net profit (the product of these) will increase. But when the
decrease in sales is more than proportionate to the increased profit
per unit, any further increase in price will be disadvantageous.
The ideal monopoly price is thus to be found precisely at the
meeting point of both these tendencies — ^the point at which
demand is reduced in the same proportion as the net profit is
increased in consequence of the higher price.

We shall endeavour to represent the position by an
arithmetical example in tabular form. Suppose that
a monopolized commodity costs the monopolist £2 a unit
to manufacture. And assume for the sake of simphcity
that the relation between price and sales is such that, with
a price of £12, 1,000 will be sold in a unit of time ; and
that every increase or decrease in price by £1 causes a decrease
or increase in sales by exactly 100 units. We may then set out
the following table : —

Selling Pnce,

Costs,

Profiteer Unit,

Turnover.

Total Net Profit.

£

£

£

Pieces.

£

22

2

20

20

2

18

200

- ■

18

2

16

400

3,600

16

2

14

600

6,400

14

2

12

800

8,400

13

2

11

900

9,900

12

2

10

1,000

10,000

11

2

9

1,100

9,900

10

2

8

1,200

9,600

8

2

6

1,400

8,400

6

2

4

1,600

6,400

4

2

2

1,800

3,600

2

2

—

2,000

—

In this case, a price of £12 is, therefore, the most
advantageous to the monopolist. He would get less profit if he
either raised or lowered the price.

If is easy to represent the fundamental features of
monopolistic pricing graphically, or algebraically. If we mark

91

THSOEY OF YALUE

ofi tlie various unit prices, p on the horizontal axis and the
corresponding quantities y, sold per unit of time, on the vertical
axis, then the locus of these points will generally describe a curve
y^f{p). The rectangle y,p represents the gross receipts, and
that part which lies to the rigid of a line at the distance a from
the vertical axis — ^where n is the unit cost of production, i.e.
y{p — - a) represents the net profit.

The expression is maximized when its first derivative with
respect to p is zero. We thus obtain

{p — a)f(p) -i-f{p) == 0,

a condition which is satisfied, as will easily be seen, when that
part of the tangent to the curve which lies between the above-
mentioned vertical line and the horizontal axis is bisected at the
point of contact. If y ==/(p) is a straight line, as with our figures,
we have simply to take half the maximum rt£t price, where sales
will be half the maximum which can be marketed without a loss.
Other questions relating to monopoly prices are similarly capable
of an easy mathematical solution. Thus, inter alia, there can be
deduced from these figures, or formulse, answers to such questions
as the various influences of general and special costs, various
forms of taxation, etc., considered on p. 72.

It is important to note that the amount of overhead costs
(i.e. costs which remain constant whether output is large or
small) has no influence whatever upon the level of the most
advantageous monopoly price. Whether, for example, a private
railway company has to pay a large or a small amount of interest
on the capital invested in construction, the height of its charges
cannot be affected, so long as these are fixed on the principle of
maximum net profit. This is obvious ; if, in the table, p. 90,
we deduct a fixed amount per unit of time (say £1,000} from
the monopolist’s net profit, then all the figures in the right-hand
column will be reduced by 1,000. Obviously, even after this
reduction, the previous maximum profit would still be
a maximum; so that the most advantageous selling price
would still be exactly £12. It is evident that this would
still apply if, for any reason (say income tax), the net profit were
reduced in proportion to its size — ^and even if the deduction
(as in the case of progressive income tax) increases more than
proportionately to net profit, so long as the rate of progression
is such that the residue (after deduction) continues to increase
wherever the profit (before deduction) would have increased.

92 LECTUEES ON POLITICAL ECONOMY

But ^erent considerations apply in the case of primo
costs-wkch increase with the output. For the sake of simpHcitv
we ^ assume that the increase of costs is exactly proportional
so that every new unit of commodity increases costs by as much
as the precedmg unit ; and so on. If, for any reason, the cost

or a umt now increases— as for example by reason nf «

ae total post. Tie

93

THEOEY OF VALUE

as tlie additional costs of production but usually less. Witb
a simple linear law of demand (on wMcb our table is based),
the most advantageous increase in the monopoly price would
be exactly half the increased cost per unit, so that if, for example,
the increase were £2 and the monopolist’s cost of production
were thus to become £4 per unit, the best seUing price would
be £13.

These propositions, which are due originally to Cournot,^
but have been developed subsequently by Pantaleoni, Marshall,
Edgeworth, and others, are of great interest both for the theory
of taxation and for the solution of the pressing problem — ^which
is daily becoming more important — of a rational regulation of
industrial monopolies, whether legal or merely dsfad^o.

The mathematical treatment of monopoly profits and their
taxation abounds in interesting and often very surprising features.
Suppose, for example, that a railway company which has a
monopoly in passenger traffic, with only two classes, second and
third, is taxed on the basis of the number of second class tickets
sold. Who wotdd suppose, at first sight, that this taxation might
make it economically advantageous for the company to reduce
the price of both second and third class tickets ? And yet Edge-
worth has fully proved ^ that, on certain assumptions, this can
be the case.

This can, if necessary, be understood without the use of
higher mathematics. For the sake of simplicity we shall assume
— an assumption very far removed from reahty — ^that ceteris
paribus the number of second class passengers is determined
exclusively by the price difference between the two classes ,* in
other words, the passengers would travel in any case, though
the difference in price decides whether they will travel second
or third class. In such a case it is in the interest of the railway
company to increase this difierence in order to force some
passengers to go over from second class to third class — ^and
thereby save in taxation. That this can always happen without
a corresponding reduction in the total revenue is implied in the
very concept of maximization — at least in most cases. A slight
change in the most advantageous price combination produces a
relatively very small reduction in traffic revenue, whereas the

^ See Principles maihematiques de la theorie des richessea. This work was
first published in 1838, but was not generally known until much later.
Translations into English and various other languages are now available.

* Papers rdating to Political Economy f vol. i, pp. 143-151, and Economic
Journal, 1899, p. 286.

94 LECTUEES ON POLITICAL ECONOMY

conesponding saving in taxation is considerable. Now a given
increase in the price difference can be brought about in three
diferent ways —

(a) by a moderate increase in second class fares and a
reduction in third class fares ;

(5) by a greater increase of the former and a slight increase
(or, at any rate, no reduction) in the latter ; and

(c) by a slight reduction (or, at any rate, no increase) in
second class fares and a greater reduction in third class fares.

By all three methods the railway company makes an equal saving
in taxation. It remains an open question, therefore, which of the
three will produce the least decrease in the traffic revenue. As a
rule it would be the first method, but in special cases the second
and even the third may be preferred, in that order.

Thus, if second class traffic is very considerable and third
class traffic not particularly elastic, it may happen that the most
profitable course would be to increase both fares (although, apart
from taxation, this increase must always reduce the traffic revenue,
since it alters the combination of prices existing before the imposi-
tion of the tax, which must be assumed to be, in those circumstances,
the most advantageous). But if third class traffic is very elastic —
so that reduced fares would attract a number of new passengers
(to the third class) — ^and the second class traffic is not very great,
then, however paradoxical it may at first sight appear, the last
of the three methods will be the most advantageous to the railway
company.

Alternatively, we might approach the problem in the following
way. Let us draw up a series of combinations of prices which,
apart from taxation, would yield the company a certain given net
income slightly less than the maximum. Geometrically, this
series could be represented by a closed curve (roughly elliptical
in shape) enclosing the maximum point ; we have then to find
the point on this curve at which the difference between the
co-ordinates (the difference between second and third class fares,
and consequently the saving in taxation) is a m gyiTmim - This
point is clearly the point of contact of the upper of the two tangents
to the curve which make an angle of 45° with the axes (cf. Fig. 7),
The same construction may then be repeated with a succession
of new curves (new series of price combinations) the process being
continued so long as the saving in taxation increases more than
the traffic revenue decreases. If the maximum point is taken as
the origin (with the direction of the axes retained) it will easily
be seen that the new point of equilibrium may be situated in the

95

THBOEY OF VALUE

first, second, or third quadrant — but of course never in uhe fourth
— according to the form and position of the curves, of which
nothing is previously known.

It must, however, not be overlooked that the study of
monopoly is peculiarly liable to be disturbed by great differences
between theory ” and “ practice ” ; and that for many reasons.

BD= ,. II „

,, III ,, ,, siter „

CE = „ n „

The monopolist is not obliged to keep so close a watch on prices
as a seller or producer working under free competition, especially
since most monopolies are in the hands of great companies, or
corporations, or States, and are managed by salaried officials
who are usually much more anxious to avoid loss by incautious
experiments than to increase their profits. Another circumstance,

96 LECTURES ON POLITICAL ECONOMY

wHch should not be overlooked, is that the growth or decline
of net profit in the immediate neighbourhood of the theoretically
most advantageous selling price is very small. This feature is
common to all real maximization, and we may easily convince
ourselves of its correctness here by reference to the above table.^
It is, therefore, largely a matter of indiSerence to the monopolist
whether his price is a little above or a little below that which
is theoretically the best — ^however important the matter may
be to the consumer.

Finally, it may be pointed out that the sharp distinction
between monopoly prices and competitive prices which we (in
common with other economists) have drawn here scarcely ever
exists in reality. Not infrequently, two or more monopolists
in the same branch of production, or in closely-related branches
(e.g. owners of various patents in the same industry) actually
compete with each other.^ We have already pointed out that
there also exists in the ordinary free competitive market a sort
of monopoly for each individual producer, and even for every
consumer — dependent upon their various geograjpJiical positions
relatively to each other and to the centres of business activity,
with consequently differing transport costs. But economic theory
has paid very Kttle attention to this aspect of the problem of
pricing.^

If there are two equally powerful monopolists in the same
branch of production then, if they operate independently y they will
doubtless depress prices, but, as Cournot observes, only up to a
certain limit — namely, the point at which each obtains the
maximum profit, under the assumption that the other neither
increases nor decreases his output beyond that limit. This new
equilibrium position can be determined without difficulty, if a
is the cost of production, by the equation

~ «)•/'(?) +/(p) == 0,

where p is the common selling price and f{p) the combined sales
of the two monopolists. The tangent referred to above (Fig. 7)
will be divided at a pomt one-third of the way along it, and in our
table (p. 90) the selling price would be reduced to £(2 + X 20)

^ Of. also my FmanztheoretiscTie UntersuchuTigen, p.l2, et seq.

* The theory of pricing under “ duopoly ” or “ polypoly ”, as they were
formerly called, was developed by Cournot (see below) and deserves attention.

A. Weber’s Z>er Standort der Indvstrie may be described as such an
attempt.

THEOEY OF VALUE

97

= £8.67 a unit with a total sale of 1,333 units— or
666 to 667 for each monopolist. In the same way, jf there are
three or more monopolists, the price will fall further, until it
finally sinks to the bare cost of production (p = a) as in free
competition. The public will, therefore, gain by the competition
of the monopolists, but the monopolists - will lose. Their own
interests compel them to combine and divide the profits — ^in
which case monopoly prices and sales will again be the same as
when there is a single monopolist.^

7. Pri-cing under the Influence of Production
Transition to Part III

Although hitherto our purpose has been to describe the
origin of market prices, on the assumption that goods exist in
given quantities for a certain consumption period, yet we have
on several occasions touched upon the effects of production on
pricing ; or rather on their influence on one another. We shall
now concern ourselves directly with this problem, and shall
consider it in detail in the next section. The older economists
drew a distinction between market price, regulated solely by
demand and supply, and ‘‘ natural price about which the
market price always oscillated, and which is itself determined
by the cost of production of the commodity. In actual fact, the
formation of prices is essentially the same in both cases, except
that the relation between supply and demand, effective on the
market, is replaced in the latter case by the relation between
production and consumption. If price equilibrium in the market
demands equality of supply and demand, then in the long run
the prices of the various commodities will be stationary at, or

^ Edgeworth, in his McUJiematical Psychics (1885) and in an essay in the
Gmrrude degli EcorurniisH, 1897 (and also the mathematician, Bertrand, in the
Journal des Savants, 1883), criticized Cournot’s reasoning, but, in my opmion,
on insufficient grounds. It is certainly true that the problem, as Edgeworth
says, will to some extent he indeterminate in the case of two, or generally
of a limited number of monopolists, whether in the same or in different branches
of production. But Cournot’s further Jissumption, quoted above, seems to me
much more reasonable than the one selected by Bertrand and Edgeworth.
The latter involves the assumption that each monopolist aims at the maximum
net profit on condition that the other does not change his price — ^an assumption
which seems to me quite unjustifiable where they both produce the same
commodity. [See Wicksell’s review {Economish Tvdskrift, 1925) of
Professor A. L. Bowiey’s Mathematical Groundwork of Economics ; a German
translation of this review subsequently appeared in the Archiv fiir Sozial-
vnssenschaft, 1927.]

LECTUEES ON POLITICAL ECONOMY

98

oscillate about, the point of equilibrium between production and
consumption — in other words the point where 'production exactly
covers consumption. We may add, in passing, that this simple
relation is all too often overlooked as, for example, when we
speak of a permanent over-production or under-consumption of
some, or even all, commodities. If this means that production
permanently exceeds consumption — ^and what else can it mean ?
— then it is manifestly absurd. After all, the capacity of our
warehouses is Innited !

If it were true that the manufacture of a commodity always
required a certain definite quantity of each factor of production
(i.e. a certain quantity of homogeneous labour, a certain area
of land of given physical properties and finally a certain use,
and corresponding using-up of capital goods — ^factories, railway
material, ships, tools, machinery, etc.), and that production did
not require any tirm (or, more correctly, that the time actually
required need only be regarded, economically speaking, as
quantities of services of labour and land, which could just as
well be supposed to be applied simultaneously as successively)
then we should have every reason to agree with Walras’ assertion
that the determination of prices, taking production into accoimt,
constitutes essentially the same problem as the formation of
prices in the market ; or is, as it were, only a variant of it.
Anyone who demands a given quantity of a given commodity
will implicitly demand a given determinate amoxmt of each of
the factors required for the production of that commodity.
On the other hand, each owner of these factors — ^the labourer,
the landowner, and the capitalist — offers a certain quantity, the
amount of which depends ceteris paribus partly on the market
price (i.e. on the rate of wages, rent and interest, etc.) and
partly on the prices of the goods which the owners of the factors
wish to acquire in return. Or, in accordance with what we have
already said, we may regard the problem from a somewhat
different point of view : the owner of a factor of production
has himself a certain direct use for it, so that what he wishes
to retain for himself may be regarded as his contribution to the
general demand for that factor. The supply must then be
regarded not as the amount which he and other owners offer,
but as the whole quantity in existence — ^for example, in the
case of labour, the whole twenty-four hours of the day — ^which

THEORY OF VALUE

in extreme cases might find productive employment. If we start
from a hyp)othetically given system of prices of ali the factors
of production, then, in the first place, we can on our assumption
deduce the corresponding prices of the finished goods (if we
regard their costs and selling prices as equal). For every such
system of prices we can then obtain, directly or indirectly,
a determinate demand for and supply of each particular factor ;
and it only remains to state that, in equilibrium, demand and
supply must coincide, or — ^if we take the word demand in its
wider sense as including the quantity which the owners of the
factors wish to consume directly at the given nrice — ^that demand
exactly equals the quantity available.

Working under this assumption, we should actually have to
deal with two factors of production only, land and labour, since
machinery and other capital goods can ultimately be reduced to
products of land and labour. If time did not play any economic
role, the employment of, and demand for, capital could be regarded
as an indirect demand for labour and land. But it is precisely
at this point that the weakness of the argument appears ; for,
since the indirect productive services must be rewarded m the
same way as the direct, the share of capital in production would
consist only of successive repayments of the capital itself, and
not of any addition in the form of interest. This agrees with the
Socialist view, according to which the remuneration of capital
consists exclusively of unpaid labour ” ; i.e. is an economically
unjustifiable robbery of the fruits of production. We must either
accept this view — ^which, however, Walras and his school refuse
to do — or we must admit that the reasoning which leads to this
result (which really ignores the existence of interest) overlooks
an important element in the explanation of the phenomena of the
real world.

This view of the position is evidently far too imperfect
to be even an approximation to reality. In the first place, the
proportions in which the various factors of production contribute
to the manufacture of any commodity are by no means given or
determinate, but may vary within certain (sometimes wide)
limits ; or, as it is sometimes expressed, one factor of jproductiorh
can always, to some extent, be svbstitiUed for another. This is
particularly true of the production of foodstuffs, which are
obtained, in a fairly uniform quality, either by extremely
extensive agriculture (for example in the robbery cultivation ’’

m LECTUEIS ON POLITICAL ECONOMY

— ^rightly or wrongly so called — of the Western States of America
or in the practice, common in Sweden, of burning off woodland
in order to secure arable land) or else by a highly developed
intensive cultivation as in China, Belgium, and the plains of Lom-
bardy. But, even in manufacturing industry, the various factors
of production, such as human labour and machinery, may be
substituted for each other to almost any extent. That is to say,
direct human labour is replaced by natural forces (in combination
with the employment of capital) and vice versa, A further
factor, which at bottom has a close connection with the above,
is that the time-element in production, so far from being a matter
of indifference from the economic point of view, is of the very
greatest importance. We cannot — at least in the last analysis —
conceive the commodity market, on the one hand, and the market
for factors of production or productive services, on the other,
as lying alongside one another, so that they could theoretically
be regarded as one. In point of time the latter always precedes
the former, and this circumstance — as we can easily understand
a priori, and as we shall show in more detail soon — ^is of the
greatest importance in actual pricing. ’ Before we can hope
for a final solution of the pricing problem we must first consider
both sides of it more carefully : the ability of the different
factors of production to replace each other, and the time-element
— or, what amounts to the same thing, the economic signi&cance
of capital. We shall consider these matters in the next part and
shall, at the same time, endeavour to solve the problem of
distribution under free competition — a problem which would
already be solved if the shares of labour, land, and capital could
be determined as simply as has been indicated above. That such
is not the case, and that the time-element plays a decisive part
in distribution, and especially in the determmation of wages,
was what John Stuart Mill wished to express by his statement,
‘"Demand for commodities is not demand for labour” —
a statement which, though fundamentally correct, has been
widely challenged and frequently misunderstood.

PART II

THE THEOEY OF PEODUCTIOX AND DISTEIBUTION

Bibliogbaphy. — There stili exists no exhausth’e presentation of
this subject on modern lines ; at least, not in an elementarj
form. Walras in his Eleinents once and for all correctly formu-
lated the solution to the problems of production, distribution,
and exchange as a whole, but his treatment of the economic
function of capital is hardly satisfactory. Bohm-Bawerk, on
the other hand, whose work Kapital und Kap'Mlzi'ns ^ — and
especially its latter part, FostUve Theorie des Kapiials^ — is
the chief source for the modern theory of capital,*d:d nor concern
himself with the synthetic treatment of the problem of produc-
tion and distribution as a whole. An attempt to combine the
work of both these writers into a single whole is to be found
in my essay, Tiber Wert^ Kapital und Recite ; and also in the
elegant but unfortunately unfinished articles of Enrico Barone,
“ Studi sulla Distnbnzione ” {Giornale degli Economisti, 1896).
P. H. Wicksteed’s succinct Co-ordination of the Laws of Distribu-
tion ^ (London, 1894) is interesting and rich in ideas — but not
easy to read. Jevons’ Theory of Political Economy contains
many instructive, though scattered, remarks on production.
The most exhaustive treatment of the subject in English,
from the modern point of view, is to be found in MarshalFs
Principles of Economics, an abridgment of which was published
under the title Elements of the Economics of Industry.

An original writer, unfortunately to a large extent self-
taught, is the German, Efiertz, who m several works (of which
the earliest is contemporary with the Positive Theorie des
Kapitals) develops views similar to those of Bohm-Bawerk ;
they are often very well stated.

We have hitherto examined, as far as it has been possible
to do, the process of valuation of the material objects or direct

1 lOapiial and Interest."]

® [Positive Theory of Capital.]

® [This IS now published in the series of Scarce Tracts, published by the
London School of Economics.]

* In his magnum opus. The Common Sense of Political Ecorwmy, he declared
— for reasons difficult to understand — ^that he desired to withdraw this
work. He devotes a chapter to the subject in the Common Sense which does
not cover the same ground.

101

102 LECTURES ON POLITICAL ECONOMY

personal services with wMch we satisfy our needs. We shall
now consider how the available stocks of goods (and, strictly
speaking, personal services also, in so far as the supply of services
presupposes a supply of consumable goods) are maintained,
renewed, and replaced. In other words, we shall now consider
production.

As has already been indicated, the problem of value and
exchange eannot be finally solved unless attention is simultaneously
paid to production. Production, on the other hand, as it actually
takes place, cannot be understood except in association with the
laws of exchange and exchange value. In reality, exchange,
and consequently valuation, enter into all production. Even
in an individuaFs production with his own resources for his own
needs there is always, at least in the wider sense of the word,
an exchange (or choice) ; the resources can be used either in
direct consumption or in indirect consumption — ^through the
medium of production. Thus, for example, anyone who has
labour available, so long as he is a free human being, has the
choice of using his working hours either for rest or diversion,
'or for productive employment in the ordinary sense. The element
of exchange naturally appears even more clearly in production
which is carried on in association with outside labour or other
factors ; or when the product is intended for consumption by
others, as is the case nowadays with the vast majority of goods
produced. In the former case, there is, of course, a direct exchange
of factors of production — ^land, labour, and capital — against
their necessary remuneration — ^wages, rent, and interest. In the
latter case, production proceeds with constant reference not only
to the volume of the output which can be obtained, but also to
the exchange value anticipated or already determined on the
market. In the majority of practical cases, both of these
considerations are present.

Production and exchange can only be separated by a process
of abstraction ; but such abstraction is an invaluable aid in the
survey and examination of what at first sight appear to be hope-
lessly complicated phenomena. For this reason, we have hitherto
assumed, in our examination of the principles governing market
values, that the supplies in the market to meet the needs of
consumers in a given period are given in advance ; although,
naturally, these supplies are continuously affected in reality

PEODUCTION AND DISTEIBUTION 103

by new production — especially in modern times with highly
developed communications. In the same way we can, and shall
for a while, in our treatment of production and distribution,
ignore the changes in the exchange value of goods which are
constantly brought about by relative changes in production
and consumption. In other words, we assume, in the first
instance, that for the society in question these exchange values
are given — as they approximately are in reality for every
individual producer, in his relation to the marker as a whole.
A concrete case of this kind would arise if a country or some
smaller area produced only one or a very few staple commodities
and imported everything else it required ; so that all exchange
values could be assumed to be determined in advance by the
market of some larger area, or even the vrorld market.

For a first approximation, we may also introduce another
important simplification. As we have already said, every owner
of a factor of production can choose between two methods of
employing it : directly or in the service of production. Even if
the relative exchange values of goods are given in advance, the
need will constantly arise for the individual to weigh up against
one another, on the one hand, the goods which he obtains, or
can obtain, in return for his productive services and, on the other
hand, the enjoyment he obtains from being able to dispose of
them freely on his own account ; as, for example, by having
more leisure. We shall, however, assume for the present that
the utility of the various factors of production, after a certain
amount has been set aside for the owner’s direct consumption,
becomes so insignificant for this purpose rhat it need not be
taken into accoimt in comparison with the indirect utility
derived from their productive employment. And this assumption
may be made without danger in the case of several factors of
production. Private owners of building sites in cities do not
usually leave any part unoccupied in order to retain it as
a promenade ground. No landowner — ^unless he were a very
exceptional person — ^would allow arable land to lie waste or
would use it as a hunting ground. Still less has the owner of
capital any choice in this respect ; in order to obtain any yield
from his capital he must employ it productively or, what generally
amounts to the same thing, lend it to someone else. The personal,
unproductive use of capital would almost necessarily be

104 LECTTJKES ON POLITICAL ECONOMY

tantamount to its partial destruction. Dwelling-houses
occupied by the owner constitute no exception to this rule, for
the only possible productive use for such capital goods is that
they should be occupied as dwellings.

Hence it is approximately true of land and capital — ^that
is to say, of the capital existing at any given moment of time —
that they enter as a whole into production. On the other hand,
we cannot reasonably say the same thing about labour. It is
a physical impossibility to work regularly for the whole
twenty-four hours of the day, and even if working hours were
limited to the maximum time which can be devoted to work
in the long run, the labourer’s position would still be so miserable
that only the most acute necessity would keep him from
converting a little of his working time to leisure purposes.
To the older economists, who generally held that the natural
and average wages of labour exactly corresponded to the
minimum of subsistence of the labourer and his family, it was
natural to regard individual labour and hours of labour as a fixed
and definite quantity, the limits of which were set only by the
physical powers of the labourer. It is characteristic that when
Adam Smith discusses the problem whether labourers are likely
to respond to a rise in wages, by devoting more time to leisure
he only does so in order to absolve them from this
charge. Nowadays, when wages have fortunately risen some-
what above the subsistence level and when the limitation
of working hours in order to give the worker an opportunity
for educational and cultural activities has become one of
the most eagerly sought objectives, especially on the part
of the workers, this assumption is no longer permissible.
Our use of it here will be only provisional, in order to simplify
the ar^ment. We must ' also remember that, in certain

occupations (particularly the manufacturing industries), the
amount of time devoted to production (especially the length
of the working day) is largely determined independently of the
individual worker, by collective agreements — ^which may be
denounced collectively, but not individually, excepting in so far
as an individual may occasionally take a day off ”,

We also ignore here the practically very important
circumstance that the mental and physical health and strength
of the worker, and consequently the efficiency of labour, are

PRODUCTION AND DISTRIBUTION 105

largely dependent on the wages received and, within certain
limits, rise and fall with the wage.

Changes in the supply of labour due to movements of
population — ^natural increase, emigration, immigration — are quite
different in kind from these and may be disregarded here. For
the most part, they are due to other than purely economic causes
and only rarely do they cause the supply of labour available
at a given moment, or in the near future, either to increase
or decrease.

In the long run, of course, not only the total supply of
labour, but also that of capital, and indeed of land also — or at
any rate the available supply — ^wili be subject to more or less
extensive changes. The same is also true of labour on the
qualitative side, in so far as changes in the manner of living,
improved education, and upbringing may cause considerable
changes in the efficiency of the available supply of labour. In
a complete analysis of economic phenomena, these changes must
of course be duly noted ; for the moment, however, we shall
content ourselves with what has been called the static aspect of
the problem of equilibrium, i.e. the conditions necessary for the
maintenance, or the periodic renewal, of a stationary state of
economic relations.

If the country or area which was mentioned above were
a unified economic unit, in which everything was produced and
exchanged with the outside world on common account, the
whole problem of production would be a purely technical one.
Given the supply of factors, it would merely be a question of
maximizing the production of the particular commodity produced
by the coimtry. If several commodities were produced — ail of
which were, in some measure, sold abroad at given prices — ^the
object would be to maximize exchange value. Again, the
distribution, whether of the direct output or of its equivalent
obtained by exchange, would be an independent question and
would be regulated by other than purely economic considerations.

The problem is different, at least at first sight, when
production proceeds, as it does in reality, under free competition
and private enterprise. In this case it is everyone’s business
to produce, not as much as possible, but as cheajily as possible,
i.e. in such a way as to maximize his net profit. This again
depends upon his costs of production or, in other words, on the

106 LECTURES ON POLITICAL ECONOMY

share of the product demanded by the factors of production.
It is therefore bound up with the problem of distribution.
For example, suppose a man has a large landed estate, but no
capital. If he were to farm the land without capital — ^by his
own labour and that of his family — ^then of course the product,
relatively to the size of the estate^ would be extremely small.
He therefore borrows capital and employs labour. But the
extent to which he does so obviously depends upon the
remuneration demanded by capital and labour in the form of
interest and wages. If he can get both for nothing, or for next
to nothing, then he wiU carry on his farming more intensively,
using more capital and more labour than he would do if the share
in the product demanded by capital and labour were so great
that — as^a result of the law of diminishing returns, which we
shall shortly consider — ^they gradually absorb the whole surplus
and perhaps leave him almost nothing. Rents would have
a similar significance to a person who possessed capital, and
possibly skill at farming, but had insufficient land to be able
to make use of them.

Again, if the producer can choose between the manufacture
of various kinds of goods — ^whose market prices are given, but
whose manufacture demands different proportions of land, labour,
and capital — ^then it will be his object to select the branch of
production which is most profitable ; and here again the relative
levels of rents, wages, and interest will, of course, be decisive.
Only when, by the influence of supply and demand, these have
reached such a relative position that two or more of these
commodities are equally profitable to manufacture, will they
be simultaneously produced. In practice, as we have already
emphasized, the problems of production and distribution cannot
be separated, but are essentially one ; production is not
a technical problem only, but technical and economic at the
same time.

Another question of great interest — ^which we propose
to examine later — ^is whether (as has often been maintained
by Socialists) collectivist production would, in a physical sense,
be superior to individualist production — leaving aside the question
of distribution ; or whether we should not, from a technical
point of view, regard both systems as leading to essentially
the same result.

PRODUCTION AND DISTRIBUTION 107

Tte agents of prodnction have usiiallv been diYided into
tlixee main groups — land, labour, and capital — of -Vv'iiicii the first
denotes the external natural forces at the service of man. In
a narrower sense, however, “ land “ may be taken to include
only those natural resources which renew themselves continuaily,
for the actual ingredients of land (such as clay, ore, peat, coal,
etc.) in so far as they are employed in production and consumption
have rather the characteristics of capital. By labour, again, we
mean exclusively human labour, whether manual or mental.
The concept of capital requires a closer analysis — and we snail
return to it later. Further, there exist important factors of
production, essentially of an immaterial kind, w^hich cannot well
be subsumed under any of these categories, but which are sui
generis, even though labour, capital (and land) are requhed for
their production. To this class belong technical inventions, so
long as they are patented or are trade secrets (otherwise they
become free goods) and also — ^if the term production is taken
in the wider sense, to include the distribution and marketing
of products — ^well-known trade marks, the goodwill of a business,
and so on." For the sake of simplicity, however, we vill keep
to the three main groups — especially since all the others, strictly
speaking, presuppose a restriction of free competition. In
accordance with our usual method we shall postpone discussion of
the difficult problem of capital ; and shall at first concern
ourselves only with land or natural resources — assumed to
be in private possession — ^and human labour ; their co-operation
in production and their shares in the product, under free
competition.

Marshall, in his Frirudjiles, has endeavoured to set up a fourth
class of agents of production, beside land, labour, and capital,
namely organization, to the important functions of which in the
modern mechanism of production he has devoted several long and
suggestive chapters of his book. But, however important it may
be to determine the economic role of intellectual progress and of
inventions and discoveries (which earher economists not
infrequently confused with capital itself), this classification sufiers
from the inconvemence that the new agency thus introduced,
unhke the old, lacks quantitative jprecision, except in some special
cases. Such a case would arise when organizing talent or technical
discovery is incorporated in certain individuals of outstanding

108 LECTURES ON POLITICAL ECONOMY

gifts or specialized education. But in that case, “ organization ”
cannot be distinguished from labour ” ; it is only a special form
of labour, and has always been so treated. Further, if inventions
exist, like a treasure of new knowledge and experience which,
by their very nature, are accessible to all, then they can only
acquire economic significance if they are preserved as trade
secrets or are protected by patents, etc. ; or unless they have
given rise to an actual monopoly for the first user — as happens
in certain cases in large-scale manufacture. In the contrary case,
they are to be regarded, as we have said, as free goods — ^such as
air, water, sunlight, etc. These enhance the whole of production
and, thereby, ceteris partbus, raise human well-being to a higher
plane, whilst themselves making no claim to a share in the product.
They have, therefore, no influence on prices.

It seems to me not altogether impossible that this defect
in scientific classification is associated with certain somewhat
hasty conclusions of Marshall which we shall discuss later.

1. Non-Cajyitalistic Proditction

Let us assume, in the first place, that production is non-
capitalistic — ^without implying that there is no capital whatever
in existence. As a rule, production without the use of any capital
is impossible, though the most primitive form of production —
mere collection of wild fruits — is a possible exception. For our
purpose it is sufiScient to assume that on account of a lack of
technical knowledge, very little capital can be employed ; but,
that it is available in such large quantities relatively to the
state of technical knowledge, that, as a first approximation,
its share in the product can be ignored. (We shall examine
later the exact conditions imder which this can happen.) We
might assume, for example, that all production — as was probably
roughly the case in the earliest agriculture in primitive clearings
— is carried through in the course of a single year, during which
the few simple tools and utensils employed are also made and
completely worn out. For the sake of simplicity we will also
assume that finished products only become ready at the end of
the year, that all wages are paid at the end of the year, and
that the workers maintain themselves during the whole of the
succeeding year on their wages so acquired. (It might be argued
that they themselves must, therefore, be regarded as a sort of

PEODUCTION AND DISTRIBUTION 109

capitalist class, but on our assumption the advantage thus gained
is so small that it need not be taken into consideration.) All
agreements between workers and landowners, or between these
two and a third party as entrepreneur, are thus based on
a division of the product at the end, of the current production
year. On what principles will this distribution take place ?

We have here two opposing groups of contracting parties —
the owners of labour, and the owners of land — who, on our
assumption, are on a footing of equality when making a business
agreement between themselves or wdth a third party. The
landowner, it is true, has hands ; but he may be unable to use
them for labour, owing to old age or from his being unaccustomed
to manual work. And, in any case, if the land is considerable
in extent, his own work may weU be insufficient to produce
enough even to repay him for his trouble and to meet the taxes
on the land. He is therefore not less dependent on labour than
labour on him. Neither are the labourers dependent on any other
entrepreneur, since, on our assumption, they are able to maintain
themselves during the whole period of production. We may,
therefore, assume either that the landowner will hire labourers
for a wage, paid, let us say, in kind at the end of the period of
production, or that the labourers themselves will hire the land
for rent which again will only be paid when the product is
completed ; or, finally, that a third person, an entrepreneur,
hires both labour and land — ^but still on condition that wages
and rent shall only be paid after the completion of production.

In order to prevent any misunderstanding, it may be pointed
out that this device is simply a logical construction without any
counterpart in reality, either at the present day or at any previous
time. On the contrary, it is reasonably certain that individual
ownership of moveable 'property (i.e. capital) and the possibility
in one form or another, of interest, preceded historically the
private ownership of land and, therefore, the possibility of
(private) rent. However insignificant the quantities of capital-
goods may have been, which could find employment with a
primitive technique of production, yet probably capital accumula-
tion and saving were, for many reasons, even less developed.
Thus, a superfluity of capital, even a relative superfluity, seldom
occurred. On the contrary, there was, as a rule, a marked shortage.
The fact that usury was forbidden in the Middle Ages did
not prevent interest from being taken in some disguised form.

HO LECTURES ON POLITICAL ECONOMY

Moreover, loan interest is only one of the many possible forms
of interest.

If we revert to modern times, we shall find that nearly every
square yard of land in most countries is in private possession
(or if in public hands is no longer available for free use), and rents
are, on the whole, steadily rising even though they fluctuate. At
the same time, however, interest is nowadays probably a greater
source of income than rent. Technical inventions, combined with
a rapid increase in population, still prevent the rate of interest
from failing below a certain amount and this yield has to
be multiplied by a quantity of capital which has grown enormously
— even in proportion to the simultaneous increase of population.

Nevertheless, the above assumption of production without
capital, or rather of production in which capital is to be regarded
as a free good, is logically conceivable and is, therefore, an abstrac-
tion which is permissible for purposes of exposition — ^in much the
same way as it is permissible in Ricardo’s theory of rent, of which
we shall shortly speak, to regard cultivation as proceeding from
better ” to worse ” land, even although, historically, the
development may in many cases have been in the opposite
direction.

A. The Landowmr as Entre'preneur.

We will first assume that the landowner is the entrepreneur.
The conception landowner presupposes that all land — or at
least the more fertile land and land more favourably situated
for trade — is already in private ownership, which is nearly always
the case in older countries. But, at the same time, the limit
has long been passed within which every new labourer will
produce the same additional product, or possibly even, by better
organization of labour (i.e. division of labour) a larger product
than that produced, on the average, by the labour already
employed on the same area of land. So long as this remains
the case — even with private ownership of land, and on the
assumption of active competition between landowners — ^there
could scarcely be any rent, properly so called, and landowners
would only receive a wage for their personal participation in
production, for example, as managers of labour. It is quite
otherwise where, as is usual in modern society, agriculture and
its related industries have already, owing to the growth of
population, reached such a degree of intensity of production

PRODUCTION AND DISTRIBUTION

111

that every additional labourer employed on the same area of
land can only produce an additional product which is smaller
than the average.

The fact that the total product of the same area of land
increases more slowly than the number of workers employed has
been put forward as a law which applies especially to agriculture
and the production of raw materials : the law of diminishing
yield, or diminishing returns. Yet this law is universal in its
application as soon as one or more of the factors of production
necessary for any particular manufacture is increased beyond a
certain limit, while the other factors remain unchanged. That
it has been possible to establish a contrary law of %nereas%7ig
returns, valid for at least some branches of industry, is entirely due
to the implied assumption that the raw materials required are to
be found in practically unlimited quantities at an unchanged, or
almost unchanged, price. If the same assumption were made
with regard to agriculture — in other words, if there were a super-
abundant supply of the best quality of land — ^then the law of
“ increasing ”, or at any rate of “ constant ” returns would
apply there too.

To claim, as Marshall does, that the former of these two
laws ” applies to nature and that the latter is characteristic of
the contribution of human labour to production seems to me
to be hardly logical. The two contributions can never be separated
altogetlier, but can only be differentiated at the margin of pro-
duction, as we shall show later on. The so-called law of increasing
returns is, fundamentally, another way of looking at the advantages
of large-scale production over small-scale or isolated production,
and it applies, in general, to all fields of production, though in
varying degrees. The law of diminishing returns is even more
universal in its application, as soon as we assume a one-sided
increase of some of the factors of production only. In a conflict
between these tendencies, therefore, “ increasing ” returns may
well prevail for a time, though “ diminishing ” returns will
prevail in the long run.

To the landowner, it can evidently never be economically
advantageous to pay an additional labourer more in wages than
the additional product obtained from employing him. But since
there is free competition between labourers, and since (as we
assume for the sake of simplicity) one labourer is as good as
another, none of the labourers previously engaged can claim
higher wages than the last one engaged ; for in that case it

112

LICTURES ON POLITICAL ECONOMY

would be more advantageous for the landowner to dismiss Mm
and fill Ms place by tbe new labourer, wbo must be satisfied
with the lower wage. On the other hand, if there is perfect
competition between employers, wages cannot sink materially
behw the amount by which an additional labourer employed
would increase production ; or (wMch is much the same thing
if the number of labourers is large) below the amount wMch
would be lost if one of the labourers already employed were
dismissed and Ms work distributed over the remainder. So long
as the landowner, by engaging one more labourer, obtains
a greater increase in production than the amount by wMch
wages are increased, it will be to Ms advantage to do so, and the
dismissal of a labourer already engaged will be, a fortiori,
a disadvantage. But if the same applies over the whole range
of producers, their competition for labourers must force up
wages imtil the difference between the additional product
obtained and the wages paid for the last labourer engaged
eventually disappears. One may therefore say, in theory, that
the additional product of the last labourer engaged will, in general,
regulate wages ; wMch can neither rise above it nor fall below
it. At the same time, it may be assumed that, owing to
competition, this additional product will be the same in all
branches of production, either in the physical sense, if ^ only one
commodity or one particular group of commodities (such as
agricultural products) is produced in all undertakings — or,
if several different kinds of commodities are simultaneously
produced at given prices, then the values of the additional
products must be equal. And, theoretically, at these wages all
the labour in the market will just find employment.

It is easy to see that what has been said above is,
fundamentally, an application of the principle wMch has already
guided us in the determination of market values. Here also, there
is a sort of exchange between the product and the wages of
labour — ^though not an exchange in the strict sense, since the
latter are a condition of the actual production of the former.
And the correspondence between wages and the additional
product of the last worker— or, as we shall henceforth call it,
the marginal productivity of labour — ^is evidently analogous to
the equality of marginal utilities for each of the parties to an
exchange— wMch regulates market price. But they are not quite

113

PEODUGTION AM) DISTRIBUTION

tlie same thing ; the difference being that, in the case of wages,
the equality is objective, but, in the case of direct exchange,
the equality of marginal utilities is subjective only.

After the payment of the wages so determined (an analogous
remuneration for the employer’s own work being supposed to
be included) there remains, as a rule, a surplus for the landlord,
which IS greater or less according to the quality and size of his
holding. ‘This surplus, whether we regard it as pure rent or a^s
rent and entrepreneurial proSt combined — of which more later
— ^will thus, on the given assumption, be the share of land, or of
its owner, in the product. In modem terminology : after the
share of one factor of production, labour, has been independently
determined (by its marginal productivity), the second factor of
production, land (or the landowner), is the residual clairmnt
who has a claim on what is left.

AJl the labourers are regarded as possessing the same skill
and strength. A merely quantitative difference in physical
strength, however, can easily be taken into account, if we treat
a particular labourer as equal to 1*1, 1*2, etc., or 0*9, 0-8, etc.,
of the average labourer. On the other hand, a higher quality
of labour cannot, as was once supposed, be reduced to t-erms of
simple unskilled labour ; in fact, at least at any given moment,
the different classes of workers represent distinct groups, each
of which is paid according to its own marginal productivity.

In order to emphasize this we will take a concrete, though
somewhat artificial, example. We will assume an area of 10,000
square miles — about the area of Wales — entirely devoted to
agriculture, and with a working population of 160,(KK) adult men.
Suppose this territory divided up into 10,000 estates of 1 square
mile each, all equally good, i.e. containing in about the same
proportion the usual kinds of land : fields, meadows, woodlands,
etc. It will then be clear that, in equilibrium, exactly sixteen
men must find employment on each one of these estates. This
distribution of labour, however obvious from the data, comes
about in reality as the result of competition on two sides, in the
way described above. So long as wages are materially lower than
the marginal product of the sixteenth labourer, it will be to the
advantage of every landowner to employ more than sixteen
labourers. But all the landowners cannot simultaneously succeed
in this object, and consequently their endeavour must result ir
a rise of wages. Again, if wages are higher than the marginal

114 LECTUEES ON POLITICAL ECONOMY

product, each of the landowners will content himself with less
than sixteen workers, which will result in unemployment and a
fall in wages through the competition of the unemployed. The
final wage, equal for all the labourers, must therefore he some-
where between the marginal product of the sixteenth and that
of an imaginary seventeenth labourer on any one of the estates
in question.

Everything now depends upon the size of this marginal
product — on the law of variation of the total product of an estate
of a given area, when the number of labourers and the intensity
of agricultural work increases or decreases. Unfortunately, this
law is practically unknown and its mathematical expression is
certainly very complicated. If, however, as is nearly always the
case in practical economic questions, it is only a question of small
variations, we can, as a rule, content ourselves with a com-
paratively simple expression ; we may therefore begin by
supposing the product to vary as a root (e.g. the square root) of
the number of labourers. If experience showed that, with the
actual labour force of sixteen workers per square mile the average
harvest was 1,600 hectolitres of corn, and the price per hectolitre
10s. then we can draw up the following table : —

Number of

ELabvbst pee Squaee Milb
Yolwme of Product,

Money value of

LaJbourers,

(Hectolitres,)

Product,

1

400 X a/~1 = 400

4,000 shillings

4

400 X 800

8,000 „

9

400 X = 1,200

12,000

16

400 X VlO = 1,600

16,000

17

400 X Vn = 400 X 4-123 =

1,650 (approx.)

16,500 (approx.)

Naturally, one would not expect that this simple relation would,
in reality, apply throughout the table. But that it does not lead
to absurd results seems to be shown by those parts of the world
where good land is still employed in very extensive agriculture,
as in newly settled countries. According to a writer in ScJiTnoller’s
Jahrhuch (1902), in Santa Fe and Cordoba (in the Argentine),
a colonist employing only one labourer was able to plough and
sow about one square mile and to harvest about 1,000 decitons of
wheat annually. For this case our table would give (400. y'S =)
about 570 hectolitres (per square mile) as the total product. But,
of course, in this case no small part of the product would be
deducted as interest on capital in the form of machinery, transport,
buildings, etc.

PEODUCTION AND DISTEIBUTION 115

If we now assume that wages are determined by the imaginary
ITth worker’s additional product, which according to what has
been said would, under these circumstances, be the minimum^
then there would be 500s. per annum per worker, or 8,000s. per
sixteen workers ; so that the landowner’s remainder would
also be 8,000 and the rent 80s. per hectare. This equality
between the total shares of the product of the workers and the
landowners is no accident, and would be the same with any
degree of intensity as soon as the law of returns has the particular
form assumed. (See p, 116.)

The following is a simple way (and one often used nowadays)
of showing the mutual dependence of rent and wages, and the
determination of their relative magnitudes : the successive
labourers employed on a given area of land are represented by

Additional

I^rodnct.

units of length on the horizontal axis measured from the origin,
and on each unit is constructed a rectangle, whose area or height
(in units of length) represents the addition to the previous product
made by the labourer in question. If the number of labourers
is large enough, the upper limit of these rectangles may be replaced
without serious error by a continuous curve — ^the curve of
productivity or gross yield. The area under this curve (bounded
by the axes and a variable ordinate) represents the whole of the
gross product secured as the number of labourers increases. The
additional product of the last labourer is represented by the last
rectangle to the extreme right, or by its height ; and since this
additional product determines both the wages of the last labourer
and those of all others, the total sum of wages is represented by a
rectangle of the same height and with a base consisting of the

116 LECTURES OH POLITICAL ECONOMY

whole distance from the origin (the total number of labourers).
The remainder of the gross yield, or the upper portion of the area
under the curve, represents the rent of the whole area cultivated.

If the number of labourers is a, then the gross product P
may be represented algebraically as a function, /(a) of the number a.
The wages of the last labourer, as of every other labourer, is then
represented approximately by the difierential coefficient f\a).
We then obtain as an expression for the rent : —

«=/(«) -a/'(a)

If, in addition, we were to assume, as in the numerical example
above, that this production function was simply a fractional
power of the number of labourers, so that F =/(a) in

which ^ is a constant and a < I then the expression for rent is
reduced to

S==P. (I - a)

that is to say, the index a also expresses the relation in which
the gross product is divided between labourers and landowners.
If, for example, as we have assumed, a = |, then both would
receive equal shares ; if a = § the labourers would receive two-
thirds of the product and the landowners would keep only a third.

The above theory of the relation of wages to the rent of
land was developed (so far as its fundamental principle — ^the
determination of wages by the marginal productivity of labour —
is concerned) as early as the beginning of the nineteenth century
by the German economist and landowner, von Thiinen. But
even earlier there had been propounded by Anderson (an
English contemporary of Adam Smith) and afterwards, quite
independently, by Malthus and West, a theory of rent, which
was adopted and developed by Ricardo in his Principles, and
which is usually associated with his name. All these theories
axe fundamentally the same. In spite of the remarkable simplicity
of von Thiinen’s theory, it coincides completely, at least as regards
the explanation of the origin of rent in the narrower sense,
with Ricardo’s theory. The latter is based, as is well known, on
two assumptions : either that agriculture is extended successively
to less fertile or less advantageously situated land, so that the
owner of the better land retains the difference in productivity
m the form of rent ; or that the land already under cultivation
is more intensively worked by the employment of increased
amounts of labour and capital, so that a similar differential

PSODUCTIOX AXD DISTSIBUTiOX

1-7

rent arises from tie dimmisned return (margiiai nroducr]' of tie
labour and capital later emplcved. In 3icardo, no^e’^^er, capital
is taken as representing a certain quanrirj of labour, directed
and maintained by tbis capital. He makes no mention, at least
in tMs connection, of increase or decrease in tbe lengtn of tne
feriod of production, wbieb, as -^e shall see later, is of decisive
importance in determining the share of capital in the product.
We may, therefore, regard thrs part of his theory as identical
with that of von Thunen.

Fundamentally, how'ever, the same applies to the first part
of Eicardo’s theory, for whether the additional product of the
last worker engaged arises from the culti^'^ation by him of pcorei
land previously uncultivated, or by mere intensive cultivation
of land already in use, is a matter of indiSerence in theory.
Which of the two occurs may be regarded in reality as the sole
concern of the entrepreneur. If the estate in question, as often
happens, includes both good land and inferior land he will in
each case select the method which is technically most
advantageous ; with essentially the same result, namely, that
every new labourer engaged, employed in the best possible
manner, will produce a smaller addition to the product.
Differences of situation with regard to marketing can, as von
Thiinen clearly shows, always be reduced to differences of costs
of transport, that is say, to costs of production, since
production must not be regarded as finished until the goods
have been brought to the market where they are 'oo be sold.

A Closer EoxLimnation of Ricardo's Theory of Eerd

Ricardo assumes for the sake of simplicity that wages,
reckoned in products or rrimns of subsistence, are constant ; because
if they should happen to rise the number of labourers would
increase to such an extent that wages would again fall either to
the absolute minimum of subsistence or to the standard which
the labourers regard as their normal standard. At that wage,
the capitalist-farmer — ^whom, in accordance with English
conditions, he assumes not to be identified with the landlord —
hires labour as far as his capital permits. On the other hand, the
product becomes his property and constitutes, after the deduction
of the capital paid out in wages, his (gross) profit. If there is a
superfluity of good land, then owing to competition among land-
owners, there cannot be any considerable rent. But as soon as

118 LECTURES ON POLITICAL ECONOMY

capital, and consequently also tKe working population, increases
to such an extent that poorer land must be taken into cultivation,
rent immediately appears ; for this poorer land yields a smaller
product to the same capital, and consequently (since wages,
reckoned in the product, remain the same) also a smaller profit.
But, owing to competition among capitalists, all capital, even
that which is employed on the better land, must now be satisfied
with this smaller profit, and the remainder will accrue to the
owners of the better land.

Simultaneously with the progressive cultivation of poorer
land and the consequent rise in the rent of the better land (i.e. of
all land under cultivation except the very worst) it will usually be
profitable to employ more labour (and capital) on the better land
already in cultivation. But since every additional quantity or
“ dose (as James Mill called it) of labour and capital yields a
smaller and smaller product, and the new capital must thus
content itself with a lower rate of interest, interest will fall all
round, even on capital previously invested and still employed,
and the surplus product which thereby arises will go to land-
owners as rent.

As wili be seen, the role of capital, in Ricardo’s opinion, is
mainly to advance wages (and to provide the necessary agri-
cultural implements, etc.). But since we have assumed that the
labourers are able to maintain themselves during the period of
production (and to prepare the necessary implements), it is clear
that the theory we have advanced above as regards the land-
owner’s share in the product is exactly the same as Ricardo’s.
How the share of the product which does not pass to the land-
owner is in fact divided between the labourers and the capitalists
is a question with which we shall deal later. On the other hand,
Ricardo and the classical economists in general pay no regard at
all to the fact that capital in many cases also advances rent.
A farmer who breeds cattle for meat, for milk, or for draught,
must pay rent for his pasturage for many years before he can
employ or advantageously dispose of the animals in question.
The same applies to an even greater extent to a person who
engages in viniculture or fruit-growing on rented land. It may
therefore be said, on the one hand, that Ricardo’s theory of rent
is too complex in relation to the single principle which it seeks
to explain, and, on the other hand, much too simple when compared
with reality. Nevertheless, his theory marked immense progress
as compared with the obscure ideas on the subject previously
extant — even in Adam Smith.

PRODUCTION AND DISTRIBUTION 119

Tlie objections wHcb were raised against this remarkable
theory in various quarters, especially in earlier times, scarcely
deserve notice. The best known is the objection of the American
economist, Carey, that, historically, cultivation did 7 iM proceed
from better to poorer land, but, on the contrary, from the poorer
to the better, i.e. from higher and therefore more easily cultivated,
though less fertile land (as for example a sandy tract) to lower
land more difficult to work, but more loamy and therefore more
fertile. This may to some extent be true, but it has no bearing
on the theory in question ; for Ricardo was only concerned
with the land which is cultivated or which can be profitably
cultivated at a certain stage in the development of cultivation.
Technical improvements, discoveries in agricultural chemistry,
and so on, may well completely revolutionize an older system
of agriculture and cause what was formerly the best land to
decline in value, or perhaps even to be abandoned altogether.
But the law of rent retains its validity, even although
the assumptions under which it operates may have changed.
The curve of returns referred to above assumes a new form, but
retains its characteristic features.

We need not waste many words, either, on the attempt of
the German, Rodbertus, the predecessor of Karl Marx, to replace
Ricardo’s theory of rent by a better one. Like Marx later, and
partly on the basis of the theory of value he inherited from
Smith and Ricardo, Rodbertus assumed that the value of the
product was wholly determined by the amount of labour employed
in its production. According to this theory, labour “ as itself a
commodity ” only obtains as a reward under free competition
its costs of production ”, i.e. the minimum of subsistence for
the labourer and his family ; the remainder — ^which Marx calls
“ unpaid labour ” — ^is taken by the capitalist. With free competi-
tion among employers, says Rodbertus, the degree of e 2 q)Ioitation
will be about the same. In industry proper, however — ^and this
is the essence of Rodbertus’ theory — ^the capitalist-entrepreneur
considers his profit as interest on two amounts of capital : that
needed for the maintenance of his labourers, and that needed
for the raw materials which he must purchase — ^the value of
which he has advanced for the period of production. But the
producer of raw materials (the landowner) has no material
expenditure of the latter kind. With an equal amount of “ unpaid
labour ” he therefore obtains a larger amount of interest on his

120 LECTDEES ON POLITICAL ECONOMY

actual capital, since it only consists of tlie maintenance of ins
labourers. If, however, he only reckons on that capital the same
amount of interest as does the industrial capitalist, there will
be a surplus, which he will consider as the rent of his land. The
most obvious objection to this theory, which appears at once
extremely artificial, is that it implies that interest and rent must
always move in the same direction, must rise or fall together —
which is contrary to all experience. That this may sometimes
appear to be the case is simply due to the fact that, with failing
interest, land, other things being equal, is capitalized at a higher
value than previously and consequently, with unchanged rent,
has a lower yield per cent on its capitalized or seUing value ;
but naturally this is an entirely secondary phenomenon.

In point of fact, Eodbertus’ theory of rent argues in a circle.
There is no reason why the ‘‘ degree of exploitation ” in different
trades between employers under free competition should be the
same, other than the assumption that the value of the product
is always proportional to the quantity of labour employed. Btit
this in its turn presupposes precisely this — ^that the degree of
exploitation is the same. In reality, the so-called ‘‘degree of
exploitation is very different in different trades, in accordance
with the different amounts of capital invested relatively to the
number of labourers employed, or (which comes to the same
thing, as we shall see) the difference in the average period of
the investment of capital. The same applies to the value of
the product in relation to the amount of labour employed in its
production.

It is evident that the Ricardo-von Thiinen theory of rent
described above is too abstract for us to be able to expect
any direct verification of it by studying the world of reality.
In addition to all other simplifying assmnptions, the part played
by capital in production, and its share in the product, find no
place in the theory as presented by von Thiinen ; and Ricardo’s
treatment of the capital aspect is too rudimentary and incomplete.
In addition, we must bear in mind that the assumptions of perfect
competition and mobility and divisibility of the factors of
production only very imperfectly correspond to reality. In
small-scale agriculture, for example, the “ last ” worker employed
is, frequently enough, the only one — ^for the simple reason that
the area of land is so small that it does not permit the employment
of more than one labourer in addition to the owner, and sometimes
not even one. On the other hand, of course, we must not forget

121

PSODirCTION AXD DISTSIBU7I0K

tlie heterogeneity of human labour and the possibility of some
substitution of the labour of women and children for that
of men.

Nevertheless, experience seems to show that the range of
applicability of von Thimen’s lav) of i/jaoes is considerable,
even in industries other than agriculture. Nothing is more
common than for employers to reply tc an increase of wages
forced upon them by a labour organization by sooner or later
dismissing some of their labourers, because it is no longer
profitable for them to carry on at full strength. If the labourers
do not support their unemBloyed comrades at the uiiioii'*s
expense — as is common, in such cases, among English trade
unions, though it is possible only up to a certain point — ^then
their competition must undoubtedly force wages do^n again
to the previous level — i.e. to equality with the marginal
productivity of labour as it is when all labourers are employed.

Further, as far as this ‘‘ law of wages is operative, the
growth of population will obviously exercise a most damaging
influence on the position of labour and of the propertyiess classes
as a whole. Particularly will this be the case under the existing
system of private ownership of land. The consequence of an
increase in the number of labourers is not only that the new
labourers will find it more difficult to earn a livelihood than
the old ones, but also that there will be a lowering of wages
all round owing to their mutual competition ; so that the
landowners’ share of the product wili be correspondingly greater.
It may be thought that experience often runs counter to this
view ; wages sometimes remain unchanged, or even rise, despite
a considerable increase in population. But the real cause here
is that the conditions of production have been materially
changed, in consequence of technical or scientific progress, and
not least under the influence of capital accumulation, which
we have not yet considered. Similarly, entirely new sources
of supply may have been discovered. If, under such circumstances,
population remained xmchanged, the marginal productivity
of labour, and consequently wages, would normally rise very
considerably. If population increases, however, both wiU sink
to their original level. In other words, technical progress, so far
as the labourers are concerned, only protects them against the
absolute fall in wages which would otherwise be inevitable,

122

LECTURES ON POLITICAL ECONOMY

whilst at the same time in increasing, frequently to a high degree,
the surplus accruing to the landlord.

The principle on which the whole theory of rent is based —
the decline in the average jdeld of labour when the number of
labourers is increased (the so-called law of diminishing returns) —
has, at all times and not least in our day, been vigorously disputed.
From the point of view of pure theory this is a matter of
indifference ; for those who deny the existence of the law must,
if they are consistent, deny the existence of rent, which they often
do when they assert that the landowners’ share of the product
is only a compensation for the labour and capital invested in the
land by them or their forefathers and is therefore interest on
capttoZ— possibly in part a repayment of that capital — and not
rent of land. The existence of rent would still remain, even on
this view, a proof of the applicability of the law. Owing to the
extreme practical importance of the question, however, we will
proceed to examine it in greater detail.

It may be thought that nothing could be easier, once attention
has been drawn to it, than to verify such a simple rule as the
relatively diminishing return of land under more intensive
cultivation — ^if in fact it is valid. It must, indeed, be quite easy
to prove it by direct experiment, and in so far as such experiments
have been made — ^unfortunately aU too few and on too small a
scale — ^the results undoubtedly tend to confirm the law. On
the other hand, it is very difficult, if not quite impossible, to
confirm the law by observing the actual yield of agriculture on
different estates. If one estate is as fertile and as rationally
cultivated as another, then the intensity of cultivation in both will
be carried to the same point, and both will naturally yield the
same return. On the other hand, every difference in the fertility
of the two estates xmder rational cultivation must give rise to a
difference in intensity of cultivation; but the result of this
differentiation will be in apparent contradiction to the law of
diminishing returns. Thus if, in equihbrium, the last dose of
labour and capital on the better land yields about the same
return as perhaps the first and only dose on the poorer land (and
previous doses on the better land therefore yield a higher return),
then on the average the more intensive cultivation will yield a
higher return for each unit of labour (“ labour and capital ”)
than the more extensive. It may consequently appear as if the
law of diminishing returns had ceased to operate and had been
reversed, although this result is really a consequence of the law.
The same applies to a comparison of the yield of an estate at

PEODUCTIOX AKD DISTRIBUTION 123

different points of time if, in the interval, more intensive cultiva-
tion has been introduced, in consequence of teclmicai progress
in agriculture, or of a rise in the price of the product.^

It is very common, even among professional economists,
to confuse the relative yield of agriculture with its profitability.
They are, however, two entirely different things. The former
is the ratio between the gross jield and the amount of labour
(or labour and capital) employed ; the latter is the difference
between that yield and the amount of wages paid (or of wages
and interest). They may therefore vary in quite different ways,
and even in opposite directions. For example, with the law of
productivity which we took as an example, according to which
the gross product increases as the square root of the number of
labourers, or P = ^ . the relative yield would heF:a='k:

and would thus continuously decline as the intensity of cultiva-
tion increases, while the rent, as we have seen, would be equal to
a, so that the profitability to the landowner would
continuously increase with increasing intensity.

As regards the foint at which the law of diminishing returns
begins to operate, we must distingmsh between the individual
and the collective, or social, points of view. From the individual
point of view, the law presumably operates from the beginning,
or at any rate from the time when the spontaneous products of
nature, such as meadows, trees, etc., obtain an exchange value.
For these products, which are obtained without labour, represent
in proportion to the labour employed an infinitely great value, and
in comparison with them every product obtained by labour will
represent a diminishing return. In other words, for the person
who has at his disposal a certain area of land, it must always be
possible by the employment of a smaU quantity of labour to obtain
a relatively greater return than by the employment of a larger
quantity of labour.

From the collective point of view, on the other hand, the services
which pioneers in newly settled countries can render each other
by co-operation in defence against wild animals or hostile tribes,
by the building of roads, and by the establishment of schools,
and the advantages to be derived from combination and division
of labour must, with an increasing population, outweigh the
inconvenience of a smaller average allocation of land to each
individual. The point at which the two opposing influences are

1 This apparent failure of the law of diminishing returns, to hold withm
certain limits, in the case of land under more intensive cultivation has been
treated by the author in greater detail in ThUnen-Archiv, vol. ii, p. 347 et seq.
and 568 et aeq. (1907-8).

124 LECTUEES OF POLITICAIi ECONOMY

balanced, and consequently tbe ofiimum density of population,
can of course only be determined in each particular case after
consideration of tbe total resources of tbe country.

B. The Labourer {or a third party) as Entrepreneur, The Profits

of the Entrepreneur,

We mig ht equally well have begun by regarding tbe labourers
tbemselves as entrepreneurs. Tbe circumstance wbicb in reality
prevents tbem from assuming this function, namely, tbeir lack
of capital, would, on our assumption, be absent, since we suppose
every labourer to be provided witb tbe means of maintaining
himself during tbe current period of production, and nothing
more is required. They are therefore free to enter, either singly
or in combination, into agriculture or any other productive
enterprise by hiring the necessary land from the landowners
against payment in kind at the end of the period of production.
The process by which equilibrium would finally be reached in
this case is fully analogous to the process described above ;
or rather it is its exact counterpart. The more land the labourers
procure, the greater will be the product ; though it will not
increase proportionally to the land taken into cultivation, but
more slowly, so that each newly-acquired acre will yield, with
an unchanged supply of labour, a smaller and smaller return.
In other words, the law of diminishing returns applies to
a one-sided increase in the amount of land. The labourers must,
therefore, if they act economically, extend their demand for
land to the point at which the additional return of the last acre
exactly corresponds to the rent demanded for it. We must,
however, assume here — ^as we did in the case of labour — ^that
all land capable of employment is of eqmlly good quality. This
assumption would not, indeed, be of much importance if we
could assume that the different kinds of land could be regarded
as of the same quality, whatever is the degree of intensity of
labour, so that better land could always be represented by
a particular multiple of the poorer land. As, however, this is
not the case, the various kinds of land must be treated in the
same way as the various qualities of labour, i.e. as so many
different kinds of means of production. ‘‘ Land and labour ”
are only to be taken as types of two independent factors of

PRODUCTION AND DISTRIBUTION 125

production. TMs metliod is valid, at least, for any given moment ;
tlie possibility of converting one kind of land into another is
a question that must be kept separate : in the same way as
we keep separate the conversion of one kind of labour into
another, by training and education.

If all the land is not at once taken into cultivation, or if,
conversely, the demand of all the groups of labour for land is
not satisfied, then it is clear that competition, in the former
case between landowners and in the latter between labourers,
would cause a fall, or a rise, in rent until complete equilibriuin
was restored. In a word, rent is here determined by the marginal
productivity of land, and conversely wages are determined by
the surplus product divided among all the labourers in the group
— ^the labourer becoming the residual claimant.

For the analysis of this problem, it is possible to employ
exactly the same diagram as in Fig. 8 with the difierence that the
units on the horizontal axis (abscissae) now represent the number
of acres of land successively taken into cultivation by a constant
number of labourers, and the corresponding ordinates (or
rectangles) the marginal products obtained. The ordinate to
the extreme right thus represents the return of the last acre
(the marginal productivity of the land) or, what comes to tie
same thing, the rent of land per acre. The large rectangle
represents the total rent and the upper part of the area under the
curve the total wages ; just the reverse of the previous case.

If the number of acres is b, the total gross product P = ^{b),
the rent per acre is ^'(6) ; then the total share of labour in the
product will be

L == ^(6) - b<f>'{b).

If, for example, the function F = ^(5) = hVb, in which k is
a constant, then L = ^kVb = JP, or the same result as we
obtained on the assumption that the gross yield varies as the
square root of the number of labourers. The reasons for this
agreement will soon be made clear.

An interesting question now arises, to which we may turn
our attention : will the distribution of the product between
landowners and labourers be the same on each of our assumptions?
Or, putting the same question in another way, if the entrepreneurs
are a third category of persons who hire labourers and land, and
pay both in accordance with the law of marginal productivity,

126 LECTURES ON POLITICAL ECONOMY

will the total of rent and wages swallow up the whole of the
product, so that nothing is left over for the entrepreneur as
such ?

This may seem evident, at least in abstract theory ; and
most economists who have employed marginal productivity as
the foundation of their theory of distribution have thought so.
On our assumptions, both labourers and landowners are free, as
they prefer, to employ their labour or land on their own account
or to hire it out to others. If the share of labour in the product
is different in the two cases, the difference, it may be thought,
will soon be cancelled out by competition, and similarly for the
share of land. At the same time, it will be obvious that the
profits of entrepreneurs as such must always tend towards zero.
Eor the work and thought which the entrepreneur devotes to the
management of production he must, of course, receive his wages
like any other mental worker. If, in addition, he also employs
property in the service of production (property which may be
land or capital, though we are not yet concerned with the latter),
then he will of course, for that reason, obtain his share of the
product (rent or interest) like any other landowner (or capitalist).
If, on the other hand, he could obtain a share of the product
merely in his capacity of entrepreneur (a share not based on either
labour or land) then it might be thought that everybody would
rush to obtain such an easily earned income.

But on the other hand, as has been sufficiently demonstrated,
the marginal productivities of labour and land do not stand
in any definite relation to the total product or to each other.
If, nevertheless, they possess this peculiar property that the
wages and rent thus determined togethei; add up to the whole
product, then clearly some other condition must be satisfied.
Such a condition exists, and is of the utmost importance, although
it has been somewhat neglected by economists. This condition
may be either that large-scale and small-scale operations are
equally productive, so that, when all the factors of production
are increased in the same proportion, the total product also
increases exactly proportionately ; or at least that all productive
enterprises have already reached the limit beyond which a further
increase in the scale of production will no longer yield any
advantage. Were it otherwise, we could no longer invoke, as we
have done, the levelling influence of competition ; for under

PRODUCTION AND DISTRIBUTION 127

siicli conditions, as we sliall soon see, free competition cannot
exist.

Tiiat tlie first condition is sufficient (tkongli not necessary)
for tlie operation of tlie law we will first show by means of an
example. Imagine a firm, say an agricnltnral enterprise, in wMcb

100 labourers are engaged on an ares of land wMcb we will imagine
to be divided into 100 units — ^no matter of wbat size. We represent
tbe annual product by P and proceed to examine wbat addition
to this product will occur if we successively increase tbe volume
of production by adding first one more labourer and then one
more unit of land. Tbe first additional product is tbe marginal
productivity of labour, in so far as we may regard tbe additional
product created by tbe 101st labourer on tbe given area of land
as roughly tbe same as that created by tbe lOOtb labourer —
a product which would be lost if one of tbe 100 labourers were
dismissed or gave up working. We represent this quantity by I
since, on our assumption, it would determine tbe amoimt of wages
paid. If tbe land under cultivation is now increased by one unit
of equally good land, so that tbe 101 workers may be spread over

101 units of land, then evidently tbe product will be increased, and
this increase is just wbat we have called the marginal productivity
of land ; for just as with labour, we can see that the increased
return which arises when tbe area of land worked by 101 labourers
is increased from 100 to 101 units does not materially difier from
tbe increase which would have taken place if tbe area of land
worked by 100 labourers bad been increased from 99 to 100 units-
But since tbe yield of tbe last unit would, on our assumption,
determine tbe rent of tbe land, i.e. constitute tbe rent of one unit
of land, we will represent it by r and then 1 + r will represent tbe
sum of tbe additional product. On tbe other band, tbe total
production has been uniformly expanded both as to tbe area of
land and tbe number of workers, and on the above assumption tbe
product should consequently have been finally increased by
exactly 1/lOOtb, so that we obtain : —

z + r = or 1001 + lOOr = P.

iUv

In other words, tbe wages of 100 workers and the rent of 100
units of land together exactly correspond to tbe original total
product.

A more general proof is tbe following. If we regard tbe
product P as a function of tbe number of labourers, a, and of tbe
number of units of land, 6, both a and 6 being regarded as

I2S

LSCT'TOiSS ON POLITICAL ECONOMY

coratinuons, tken tie marginal produoti-^ties may be expressed by
tbe parciai deriTatives of P with, respect to o and 6 ; therefore,
if the condition is to be satisfied, ve must have

cP , ,dP
°da ^db

= P

- •

a partial diSerential equamon. the genera! integral of wKicli is
knoTm to be ; —

iz ■which /( ) is an arbitral^ functions i.e. P must be anhcmogenous
and linear function of c and K Among the inSnite number of
functions which satisfy this condition, we may give as an example
P = 5^5 in which the indices a and ^3 are two constant fractions
whose sum = 1. If we substitute r^ia lor a and 73ib for 6, then F
becomes mP. i.e. large-scale and smaR-scale prodnction are equally
productive.

If, on the other hand, P retained the same form, but
a -f ^ > 1, so that P was a homogenous function of a and b
but of a riigh&r degree than the hrst, we should obtain

In other words, if, in an enterprise which becomes more productive
the larger the scale of operations, the labour and land employed
were both paid in accordance with the law of marginal productivity,
then the sum of their shares would exceed the whole product, so
that the entrepreneur would suSer a loss.

This result is connected with the circumstance that under
such conditions equilibrium is impossible. Large scale operations,
being more profitable than small scale, can here ofier better
terms to landowners and labourers (or cheaper goods to the
consumer) ; and if the smaller entrepreneur seeks to compete, his
profits will in fact be negative ; that is, competition will drive
him out. But} the same will also happen in the case of the large-
scale enterprise as soon as another on a still larger scale is
established.

The converse ■will be the case if cl -j- ^ 1 5 in other words,

if an enterprise is more profitable the smaller the scale of its
operations. We shall then obtain

P>

^ a '

PRODUCTION AND DISTRIBUTION

129

that js, the entrepreneur as snch will necessarhy obtain a profit,
but for that very reason everybody will want to be an entrepreneur,
with the result that all enterprises will ultimately be split up into
small individual units.

The first assmnption, that the relative yield of production
is independent of the scale of operations, is, of course, very
seldom realized as a general principle in a given branch of
production ; the scale on which an enterprise operates nearly
always has some influence on its average product. This is not
to say, however, that its influence always works in the same
direction. On the contrary, as a rule the best returns are obtained
at some particular scale of operations for the firm in question ;
if this is exceeded, the advantages of centralization are outweighed
by the increased costs which are encountered when larger areas
must be exploited for the provision of raw or auxiliary materials,
or else for the marketing of the product. This scale of operations
is, under the given circumstances, the optimum ” towards
which the firm must always, economically speaking, gravitate ;
and as it lies at the point of transition from ^‘increasing’’ to
diminishing returns ” (relatively to the scale of production)
the firm will here conform to the law of constant returns.^ Wages
and rent will continue to be determined by the law of marginal
productivity and the profits of the entrepreneur must tend
towards zero — all on the assumption that the enterprises in
question, in one and the same branch of production, are
sufficiently numerous to compete with each other efiectively.

Let a and h represent respectively the number of units or
labour and land employed in the enterprise in question, and
I and r the wages and rent actually paid, expressed either in
money or product ; and let F represent the annual product
expressed in the same unit of value. Then, the ratio, h, between
returns and costs of production in this enterprise will be : —

m .

aA + b.r

If an additional labourer is employed, this equation will be
changed to ; —

h - P +

{a -f* 1)-^ ”t"

^ This simple method of presentation was pointed out to me in a letter
from Professor Davidson.

130

LECTUEES ON POLITICAL ECONOMY

where is the marginal productivity of labour in a him of tills
particular ske. If the supply of land is now increased in its turn
by one unit, we obtain : —

2 +

where P?, is the marginal productivity of land. So long as tins
fraction can be continually increased by the introduction of one
more labourer or one more unit of land (so that ^ etc.),

tne enterprise has evidently not yet attained its optimum size.
The latter is first reached when k can no longer be increased —
which clearly occurs only when the numerator and the denominator
of the fraction are increased in the same proportion, i.e. when : —

P

a.l + 6.r

(I),

where P^ and P^ represent the additions to the product P which
arise from the employment of one more labourer, or one more
unit 01 land — in other words, the (variable) marginal productivities
of labour and land. Even if there is a profit for the entrepreneur
{k > 1) wages and rent must be proportioml to the marginal
products ; as is evident, since labour and land are assumed to
be substitutable at the margin.

If, even when the firms have reached the optimum scale,
they are still numerous enough for perfect competition to be
maintained, then wages and rent must be forced up to the point
where the entrepreneur's profit becomes zero, either because new
entrepreneurs enter the industry, or because those already engaged
in it will establish more than one concern each. Indeed, strictly
speaking, this must take place whenever there appears the smallest
possibility of a profit. (This change will not affect the most
profitable size of the firm, for since P, P^ and P^ are functions
of a and h only, the same values a and h will satisfy the equations
(1) even if I and r are increased or diminished in the same pro-
portion, Full equilibrium is thus only reached when k=l and
when, consequently, Z = P^ and r = P^ ; when further

P (1,1 -|- b,T.

This is the result previously obtained on the assumption that the
average product was entirely independent of the scale of produc-
tion. With the firm at its optimum size, the entrepreneur no
longer receives a profit ; hut he is secured against the loss in

PRODUCTION AND DISTRIBUTION 131

whicli lie would be involved if he were to expand beyond that
size, or not to expand up to it.^

If, "on tie otter hand, tie law of increasing returns applies
witiont qualification — or, wiat amounts to tie same tiing in
practice, if tie optimum scale of tie enterprise is so iigi, and
the number of such enterprises consequently so small, that tie
owners can easily combine in a ring, trust, or ca^el ; then there
no longer exists any equilibrium of tie kind we are here
considering. Tie wide industry will be dominated by a more
or less completely monopolistic association and all smaEer
concerns will disappear.

In reality this is not exactly what happens, but for several
reasons, and especially because of tie local character of the
finn and its market, a small firm situated, it may .he, in some
geographically remote place, may sometimes exist alongside
much larger firms in other places. This, however, will not
prevent the larger firm from enjoying advantages due to its
better organization and division of labour, which tie smaller
firm lacks, and from yielding on that account, in addition to
wages and rent (as well as interest) a true profit, or perhaps
more correctly, a monopoly profit. The large firm cannot be
deprived of this profit, because any attempt on the part of tie
smaller enterprise at effective competition outside its own local
area would be fruitless. If, on tie other hand, tie smaller
enterprise, by a great economic effort, were to establish itself
on tie same footing as the large enterprise, this would only
lead to the min of both, since there would be no room in the
market for two such large concerns in tie same industry. Thus
tie large enterprise has an actual monopoly simply because it
came first on the scene, and this monopoly may be as good as
a monopoly which is legally established.

We must not forget that the modern development of
communications necessarily increases the advantages of large-
scale operations and tends to hasten their ascendency. Agriculture
is the industry wi'ch, both in the past and in the present, has
offered most resistance to this tendency, though there are some
indications that future developments m this industry may also
be in the direction of large-scale operation.

^ The basis of this ailment is due to Enrico Barone ; of. Walras,
J^lements d'economie jpolittqiie pure, 3rd edition, p. 489 et seq.

132

LECTURES ON POLITICAL ECONOMY

Tlie objection whicli lias been raised to the effect that small
farming on co-operative lines — by the establishment of buying
and selling associations, co-operative dairies, the use in rotation
of expensive machinery hired or purchased by the association —
is a means of overcoming these difiSculties is rather an argument
in favour of the above assumption ; for these associations m fact
bring about a kind of large-scale operation, and this first step
towards association, once taken, will, in all probability, soon be
followed by others.

But, although more or less monopolistic enterprises constantly
gain ground, there still remain fields of activity in which
free competition prevails — either where large and small-scale
operations are approximately equally profitable or where the
most profitable scale of production is, on the whole, fairly small.
In such fields our theory appKes fully ; there is normally no
entrepreneur’s profit in the narrow sense. In production without
capital, wages and rent would alone share the product and their
respective shares would be determined by the marginal
productivity of labour and land — ^whether labourers, landowners,
or anyone else, act as entrepreneurs. And, so long as such a field
of activity of any considerable dimensions exists, it will set the
standard of wages and rents in the whole field of production,
since the entrepreneurs who enjoy monopolistic advantages wiU
not give to labourers or landowners more than they would be
forced to give under competition. In the latter concerns, more-
over, the law of marginal productivity stiU applies, in the
sense that the shares of labour and land remain projxyrtional
to their marginal productivity (cf. the paragraph in small print
on p. 129).

Between rent and wages there is thus, in every case,
a practically complete parallelism. No special theory of rent is
necessary, but every acre of land may be treated in just the
same way as a labourer ; the owner of land under a system
of private ownership of land must be rewarded for its contribution
to production just as the owner of slave labour would be paid if
slave labour were hired in the market. Almost all production
is the result of land and labour combined ; neither, at any rate
not land, can wholly be dispensed with in production, but either
can, at the margin of production, replace the other ; and it is
true of both that a one-sided increase of one, with an unchanged

PEOBUCTION AM) DISTRIBUTION 133

quantity of the other, will lead to an ever smaller and smaller
increase in the product.

With these reservations and limitations, this additional
product will determine the magnitude of both wages and rent.
The total contribution of labour or of land to the product cannot be
ascertained. But this total contribution has no real importance,
since, as has been said, neither of them, and certainly not labour,
can be productive alone. Only at the margin of production, that
is to say, at the point where equilibrium is reached, does the
contribution of either assume an independent character, and it
then determines not only the reward of those factors which
begin to participate in production at that point, but also, owing
to the law of indifference or competition, wages (and rent) as
a whole.

It need only be said that the above applies, as will easily
be seen, both individually and generally — according as we
consider the additional product created by an individual
productive enterprise when it employs one more worker or one
more acre of land, or as we consider the addition to the whole
social product when the total amount of labour or of cultivable
land is increased by a small amount. Yet we must not forget
that the law of ‘‘ mcreasing returns also applies to some
extent to society as a whole. If a uniform increase both of the
land and population of a country were to occur, say by a political
union of two countries of much the same natural conditions, or
simply by tbe removal of a tariff wall between them, then
it is certainly not impossible, but even very probable, that the
increased social division of labour would enlarge the combmed
product more than proportionately to the growth in the size
of the society. Still more would this be the case, of course, if
conditions had been different in the two areas ; but that is,
in part, a different question. With this last reservation, however,
the diagrams and formulae which we have used above apply,
if the quantities taken represent the whole of the labour and
land existmg in the society. The importance of this observation
will become clear in what follows.

C, The Influence of Technical Inventions on Rent and Wages.

We are now in a position to make a theoretical examination
of a subject of the greatest practical importance — ^the influence

134 LECTURIS ON POLITICAL ECONOMY

of teclmicai aad meclianical inventions on the distributive
shares of the factors — especially wages. Naturally, we cannot
give a complete answer to this question until we have discussed
the role of capital in production. Machinery, however, in addition
to having the quality of being, or representing, capital (which
we shall define in greal^r detail later), also possesses the quality
of modifying the conditions under which labour and land replace
each other at the margin of production. In other words, it may
alter their relative marginal productivities and thereby, according
to our theory, their shares in the product. It is with this
characteristic of machinery that we shall now concern ourselves.
For the time being, we shall not permit this complex problem
to be further complicated by allowing the third factor of
production, capital proper, to enter. In other words, we shall,
regard machinery as indirectly employed (not as saved or stored
up *") labour and land.

The most striking feature of machinery is that it replaces
human labour, i.e. allows us to produce the same quantity
of goods as before with less labour ; and consequently, as a rule,
more goods with the same labour. On the one hand, it may
be thought that the greater productivity of labour ought to bring
about, or at least render possible, the payment of higher wages ;
on the other hand, it is commonly supposed to render a number
of labourers superfluous, so that competition among the
unemployed would depress wages. It would seem, therefore,
that two opposing tendencies come into operation simultaneously,
and that, according as one or the other predominates, the
introduction of machinery will benefit labour or injure it.
Opinions on this point have varied in the course of time.
Formerly, under the influence of the mercantilist theory, no
doubt at all was felt that labour-saving machinery took the
bread from the mouths of the workers, and not only they, but
also the authorities, stubbornly resisted* the introduction of
machinery in one or other branch of manufacture. The victory
of the physiocratic school produced a sudden change, for according
to its theory, especially as formulated by J, B. Say, goods must
always ultimately exchange against, and therefore constitute
a demand for, other goods ; an increased productivity of labour
should of itself lead to an increased demand for goo^ hitherto
not consumed, or consumed only on a small scale, and therefore

PRODUCTION AND DISTRIBUTION 135

for labour to produce them. Hence, machineiy would, at most,
cause temporary unemployment and inconvenience to certain
groups or labourers. In the long run it would be beneficial,
would lead to increased opportunities for labour, and would
raise and not lower wages. However, this optimistic view received
a set-back when Ricardo, in a special chapter on machinery ”,
in the third edition of his Prindjiles, proved irrefutably, as it
was thought, that the introduction of machinery and other
labour-saving methods may be economically advantageous to
employers even when it does not involve an increase, but on
the contrary involves a decrease, in the ske of the product ;
provided that the net profit of the entrepreneur simultaneously
becomes greater. In such a case the labourers could not be
compensated by an increased demand for other commodities.

The question has remained in this somewhat unsatisfactory
position until the present time. The theory of marginal
productivity will enable us, I believe, to put it on a firmer
foundation, and to substitute something better for this vague,
and even in parts erroneous, analysis. Indeed, the expression
productivity of labour ” has no comprehensible meaning when
it is applied to production as a whole, for this is, as we have
seen, always the combined result of labour and land. It is,
therefore, the common productivity of labour and land which
is increased by machinery. How much of the increase is to be
ascribed to the action of one or the other factor cannot be
ascertained, and is further of no importance in regard to their
respective shares of the product. In this connection, marginal
productivity alone is the determining factor. But an increase in
the total product as a result of technical changes in the processes
of production need not by any means lead to an increase — ^and
certainly not to a uniform increase — ^in the marginal productivity of
both factors of production. It may be that the marginal product
of one of the factors decreases whilst the marginal product of
the other increases all the more ; either the marginal productivity
of labour may increase at the expense of land, and consequently
wages at the expense of rent, or conversely rent may increase
at the expense of wages. Examples of the former kind are
perhaps to be expected where, owing to some invention, the
existing supply of natural energy is, as it were, increased ;
certain hitherto neglected sources of energy, such as coal or

136 LECTUEES ON POLITICAL ECONOMY

water-power, find new uses formerly useless land is rendered
fertile, with or without preliminary treatment ; forestry is
replaced by market gardening, and so on. In such cases it is
possible, or at any rate conceivable, that rents will Mi both
absolutely and relatively, sc that the whole profit from increased
production, and even more, will accrue to labour. It may,
perhaps, be objected that the introduction of such changes,
being contrary to the interests of the landowners, would never
be allowed to take place ; but this objection, as we shall soon
see, cannot be maintained. The contrary result might be feared
where an invention vTimG fade renders labour superfluous
without calling into existence any new natural forces — ^as, for
example, in the case of certain agrieuitural machinery for sowing,
harvesting and threshing, etc., which replace human labour on
a large scale by draught animals, or other non-human forces,
without changing the actual method of tilling. Here, too, an
increase in the total product is not excluded — ^we shall see later
that in theory it must always occur. If, for example, the same
product is obtained with a smaller number of labourers, then
the displaced labourers must, nevertheless, always be able to
produce something, so that the final result is an addition to
production. But this result may none the less co-exist with
a decrease, and even a considerable decrease, in the marginal
productivity of labour, and consequently in wages.

The objection has been made, it is true, that under such
circumstances the landowners neither would, nor could, consume
their increased rents directly, in hind. They would therefore
direct their consumption towards luxury articles and thereby
increase their demand for human labour, so that wages would
again rise. But this circumstance is, as will easily be seen, only
of secondary importance. It may more or less modify the first
probable result but can scarcely reverse it. And the objection
clearly has no force if we maintaia the assumption made above,
of an economic society which, from its natural circumstances,
only produces one or a few staple articles — ^and which must
consequently procure all other commodities from other places
or countries at exchange values which are determined in the
world market, independently of anything they may do. If, for
example, the landowners obtain, in exchange for their increased
rent in corn, the most elaborate manufactures from other places

PROBUGTION AND DISTRIBUTION 137

or countries, this will benefit their own labourers, more or less
bound to the soil, just as little as if they had consumed it in
kind — ^as fodder for racehorses, hounds, and so on. In neither
case can there be any question of compensation to the workers
in the form of another demand for labour.

On the other hand, it appears on closer examination — and
the fact seems to me of great interest — ^that the objection raised
by Ricardo is theoretically unteimble, A diminution in the gross
product, or in its value (assuming, as before, that prices of
commodities are given and constant), is scarcely conceivable
as a result of technical improvements — ^under free competition.
This appears to be self-evident ; for in that case anybody would
be able, with the given means of production, to bring about at
some point an increase of the product and thereby reap a profit
as entrepreneur. Ricardo has here failed to draw the final
conclusions from his own assumptions. It is true that in the
passage referred to his starting-point is capital — which he
divides into circulating capital (or wages-fund) and fixed capital.
But his reasoning is, as he himself says, equally applicable
under our simplifying assumption of production without capital,
and in both cases it is open to the same objections.

Let us assume that the introduction of labour-saving
agricultural machinery (haymaking machines, horse-harrows,
etc.) has made a predominantly pastoral agriculture more
profitable, other things being equal, than arable farming ; so
that the value of the product, though certainly less, produces
a larger net yield, owing to the saving of labour. The direct
consequence must then be that one or more farmers will go
over to the more profitable form of production. If all were
to follow their example, there would certainly be a more or less
considerable diminution of the total product (or of its exchange
value), bvt this does not happen. For as soon as a number of
labourers have been made superfluous by these changes, and
wages have accordingly fallen, then, as Ricardo failed to see,
the old methods of production — ^in this case the old arable
farming — ^will become more profitable ; they will develop, using
labour more intensively and absorb the suiplus of idle labourers.
It can be rigorously proved that equilibrium in this case
necessarily presupposes a division of production between the
old and the new methods so that the net profits of the entrepreneur

138 LEOTUEIS ON POLITICAL ECONOMY

will be equally great in botb brancbes of production and tbe total
product, or iis exchange value, will reach the maximum physically
possible, and will thus finally increase, and not decrease.

We shall first show this by means of an example. Assume
ten large estates, all of the same size and with the same natural
* advantages and each employing by the old methods 100 labourers.
Wages are, say, 500 shillings, the gross product of each estate

100.000 shillings, and the net profit of each owner consequently

50.000 shillings.

Let us now assume that one of the landowners adopts the
new method. He dismisses 50 labourers, but with the help of the
remaining 50 he obtains a gross yield worth 77,500 shillings, so
that his net profit is 77,500 — (50 X 500) == 62,500 shillings.

Of the 50 unemployed labourers, let us assume that 45 are
absorbed into the nine other estates, or five in each, and that of
these additional five workers: —

No. 1 produces an additional value ot, say, 500 shillings.

No. 2 „

»> »»

tt

„ „ 490

tt

No. 3

ft ft

tt

.. 480

tt

No. 4 „

tt tt

tt

„ 470

tt

No. 5

ft tt

tt

» » 460

tt

For five workers, total 2,400

tt

At the same time, the consequence must be that wages will
fall aU round, let us say to 450 shillings, in which case the owner
of the first estate may find it advantageous to re-employ, say,
five of his previous employees. We will assume, for the sake of
simplicity, that their additional product will be equal to the
above, or 2,400 shillings. The final result will be : —

Qrosa

Prodmct.

Wages.

Net Profit.

In each oi the nine

Shillings*

ShiUings.

ShiUings.

old estates

In the “ new ”

102,400

105 X 460 = 47,260

66,150

estate after re-
employing five
labourers.

79,900

66 X 460 = 24,760

66,150

The total gross product, which was formerly exactly 1,000,000
shillings, will now be : —

(9 X 102,400) + 79,900 = 1,001,500 shiUings.

Thus the result is that the total gross output has been increased
and not diminished, and since the old estates, which employ
more labourers, are more favoured by the fall in wages, they will

PRODUCTION AND DISTRIBUTION 139

finally have tlie same profit as the “ new ” estate, so tliat tliere
no longer remains any inducement to go over to the new methods-
In a more general form the proof is as follows : Let Pig, 9
represent the old method of cultivation and the Fig. 10
the new, in which a smaller number of labourers are employed
on an equal area of land, and in which the gross product is also
smaller ; the net profit, however (the upper part of the area under

the curve), is greater. Let Us suppose that one or more land-
owners go over to the new method of cultivation. A number of
the dismissed labourers will then seek employment in the estates
working on the old methods. As they are so few, they will produce
on each of these estates an additional product almost e^mUy as
greal as that of the last of the labourers previously employed,
and since the net product of the estates adopting the new method
is greater than previously, the total gross prodtict must comeguently

140

LECTURES 02s' POLITICAL ECONOMY

have increased. At tlie same time, marginal productivity and
wages Lave fallen somewLat, so tLat the landowners’ share, even
in the old estates, becomes somewhat greater than before. The
same process will repeat itself each time an estate goes over
to the new method of cultivation, and since falling wages in
themselves bring a larger profit to the owners of the old estates,
as the number of labourers is greater in them than in the new,
then sooner or later a point will be reached at which the net profit
will be esactly the same in both, and every inducement to a
further transition from the old to the new will therefore disappear.
At this point, too, the total gross product will have reached the
masimum.

This really follows directly from what has been said, but
it can also be directly proved in algebraic form. If x and y are
the number of labourers per acre on the first and second methods
of cultivation respectively, and the productivity function in the
one case is j{x) and in the other d>{y ) ; and if we assume that
m acres are cultivated on the first method and n acres on the
second, then we must look for the conditions under which the

expression ,

mfix) +

reaches its maximum value if, at the same time,

and

m + n =: B
mx-t-ny^ A

where B is the number of acres and A the number of labourers
available for the industry in question (here agriculture) as a whole.
By difierentiation and elimination (the partial derivatives of the
first expression being put = 0) we can easily obtain the two

and

f{x) - 7j\x) = ^{y) ~ y^'(y),

of which the former indicates that when the gross product is a
maximum the marginal productivity of labour, and therefore
wages, will be the same in both types of production. The second
equation gives the same condition for rent per acre.

Thus, although at first sight the going-over of some firms
to the new method of cultivation seems to dimiTiiph the total
product, actually the total product is maximized ; hU at the same
time wages TiecessarUy fall, so long as we assume that the gross
product is less in the estates cultivated by the new method than
in those cultivated by the old.

PEODUCTION AND-DISTEIBTJTION

141

Nor is tke result any different if we assume that wages
are already at the subsistence level (and cannotj according to
the usual view, fall lower). In reality, wages can not only be
forced below it for a little, but can remain below it indefinitely,
if the labourers and their families can make up the difference by
poor relief, as happened in England to a great extent at the end
of the eighteenth and the beginning of the nineteenth centuries.
If we assume that the available supply of labour must, under
any circumstances, be somehow supported by the landowners,
it would in fact be more advantageous for them to reduce vrages
to the point to which they would tend to fall as a result of free
competition, and to add, by charity, enough to bring up their
incomes to the necessaiy Tniui-nmim ; it would be better to do
this than to insist that every labourer employed should earn the
subsistence wage. Especially after the discovery of a technical
improvement of the kind in question, such minimum wage
regulation might have the result that many labourers would
be unemployed and, with their fa mili es, would become entirely
dependent on poor relief.

Although we have so far only concerned ourselves with some
of the forces at work, we may nevertheless proceed on the
provisional conclusion that free competition is normally a
sufficient condition to ensure maximization of production. But
this maximization may very weU be associated with, and even
be conditional upon, a reduction in the distributive share of
one of the factors of production — ^in this case, labour. This
shows the serious error of those who see in free competition
a sufficient means for the maximum satisfaction of the needs
or desires of all members of society.

It might further be supposed that a result which led to
a reduction in wages could not at any rate arise with the labourers
as entrepreneurs ; and, on the other hand, a change in production
that led to a reduction in rents would never be acceptable to
landowners as entrepreneurs ; both of these results are, however,
quite possible under free competition. To the individual
entrepreneur who encoimters a certain market rate of rent or
wages, a technical improvement which increases his net return
is in itself always economically advantageous. That it should
have the contrary effect when all entrepreneurs follow suit
does not, in general, affect the manner of procedure of the

142 LECTUEES ON POLITICAL ECONOMY

individual, unless agreements, cartels, etc., take the place of
free competition. In any case it is to be noticed that production
(so far as our assumptions hold) reaches its maximum, from
a technical point of view, with universal free competition.
Co-operation between workers to raise wages and between
employee and landowners to lower wages (in the course of which
some land must remain uncultivated) would both lead to '
a diminution of product, and only if co-operation results in social
collectivism could the maximum product, physically and
technically possible, again be reached.

An interesting example of this is afforded, if I am not mistaken,
by conditions in Swedish forest districts, for example, Norrland
or SmMand. If forest products rise in value, it may very well
be that farming, which had previously been possible in such
areas on occasion, will no longer be profitable, and from the
point of view of the landowner it will be better to abandon farming
and to plant trees on his fields. And this despite the fact that
forestry obviously cannot support nearly so many men on a
given area as even the poorest farming. That the owners of the
land may acquire great and unearned wealth in this way, whilst
wages are at the same time forced down by the supeiuity of
labour is a grievous wrong which should certainly be righted.
But the sup^sed conflict between a private and public economic
interest, which some people have found in these circumstances
and which they have even sought to remedy by legislation, does
not, if our observations are correct, exist. Indeed, the total
national product will probably be greater if forestry is every-
where free to expand wherever — from the point of view of private
economic interests — it is most profitable ; and the superfluous
labour (in so far as it cannot be absorbed into the industries
based on forestry) seeks employment in those districts which
continue, by reason of their natural advantages, to practise
farming.

In other words, the evils here requiring a remedy relate
exclusively to the problem of the social distribution of income, and
not to that of the economically most advantageous method of
production.

Exactly the same is true of the “ parasitic ” occupations
much discussed in recent years, those in which the labourers,
usually women and children, do not receive a living wage, but
are partially supported by others (parents, relations, etc.). It is
said that, in the interests of society, such occupations should be

PRODUCTION AND DISTRIBUTION 143

forbidden \9here tbe employers will not, or cannot, offer Ml wages.
Yet tbe only result of doing so would probably be tbat those now
employed in them, far from having their position improved, would
have to rely entirely on the support of others.

On the whole, it is a mistake to regard as obvious — as is
so often done — ^that all healthy persons capable of work must
be able to live by their labour dlone, unless the country is (in the
vulgar sense) overpopulated. On the contrary, it is quite
conceivable that the total output of a society may be large enough
for all, but that the* marginal productivity of labour is none the
less so small that labour has only a slight economic value. Even
in a socialist state, under such conditions, the wages paid would
only correspond to a part of necessary expenditure, whilst the
rest would have to be found from the rent and interest of the
society.

This, of course, does not exclude the possibility that the
great majority of inventions and technical improvements may
be beneficial in both directions ; i.e. may in themselves tend
to increase the marginal productivity of both labour and land,
together with their share in the product. According to the
ordinary rules of probability there is, indeed, an overwhelming
probability that they will do so, as soon as the increase in total
productivity becomes sufficiently general. If the colossal advance
in all fields of production during, let us say, the last two centuries,
has nevertheless brought only a relatively slight, and in many
cases very doubtM, improvement in the conditions of labour,
whilst rent has successively doubled and redoubled, the primary
cause, as we have said, is to be found in the one-sided increase
in one factor of production, namely labour, owing to the great
increase in population during that period. Such an increase
must, other things being equal, continually reduce the marginal
productivity of labour and force down wages ; or — ^what comes
to the same thing, though the connection is easily overlooked
on a superficial view — 'prevent the otherwise inevitable rise in
wages due to technical progress. Unfortunately, collectivism
cannot provide a remedy for this evil created by the labourers
themselves — ^at any rate not in the long run.

It is scarcely possible to discover a simple and intelligible
criterion which will indicate whether a change in the technique
of production is in itself likely to raise or to lower wages. But
in accordance with what we have said in our criticism of

144 LECTUEES ON POLITICAL ECONOMY

Ricardo’s theory, it may be asserted that, whenever the primary
effect of a change in production is to cause employers to reduce
the number of their employees without their having been
compelled to do so by a rise in wages, it is a sign that the marginal
productivity of labour has fallen and a larger or smaller ultimate
reduction in wages will probably ensue. On the other hand,
a technical improvement which favours labour must reveal itself
from the beginning in an increased demand for labour and higher
wages in much the same way as if, in the example on p. 137,
technical improvements had tended to make arable farming
more profitable than pastoral, instead of vice versa. But what
we have said here applies maioly to wages and rent, in relation
to each other. The appearance of capital in the field of production
introduces, as we shall see below, certain modifications in our
conclusions, without, however, rendering them invalid as a whole.

2. Capitalistic Prodvicticn
A, The Concept of CapiMl.

We now come to the third group of factors of production
— ^those which are commonly included m the term capital
To give an account of the real nature of capital, its role in
production and the grounds upon which its owners, like the
owners of land and labour, claim a share in the product, is
considerably more difficult than with the other two factors
and has led to innumerable controversies among economists.
One of the chief difficulties has been the varied and changing
forms which productive capital assumes in reality. In the
ordinary sense of the term, it includes all auxiliaries to production,
with the exception of natural forces in their original form, and
direct human labour. Thus, in the first place, it includes the
houses and buildings in which work is carried on or which are
otherwise necessary to business ^ ; the implements, tools, and
machinery with wMch it is conducted, and also a further very
important group — livestock. Capital also includes the raw

materials which are worked up, and finally — ^not the least
important category— the provisions and other commodities

what extent dwelling-houses and durable objects of consumption
are to be reckoned as capital is a disputed question to which we shall return.

PRODUCTION AND DISTRIBUTION 145

whict miist be saved up or otherwise held ready, if labour is to
be supported during the period while work is in progress. This,
of course, is the commonly accepted sense of the term. Some
^mters, such as Stanley Jevons, go so far as to regard the last
item as fundamentally including the whole of capital — that is
to say, all capital in its form of free capital, before it is invested
in production. This is, however, as we shall soon see, too
one-sided a view of the matter.

At first sight all these requisites have only one quality in
common, namely that they represent certain quantities of
exchange value, so that collectively they may be regarded as
a single sum of value, a certain amount of the medium of exchange,
money. This also appears to be the reason for the name capitaij
for the word was originally understood tc mean a sum of money
lent, cavitalis pars dehiti — ^“the principal of a loan as opposed to
the interest. But, since the yield of production is also measured
in value temG^, capital, like loaned money, has the peculiarity
that its share in the product — interest — ^is the same hind of thing
as capital itself ; interest is an organic growth out of capital,
a certain percentage of capital, whereas wages as against labour,
and rent as against land, are quite heterogeneous things. Land
certainly has, especially in our day, a capital or money value,
of which rent may be said to be a certain percentage, say
3, 4, 5, or more per cent, but this is, as we have already said,
somethmg derivative and secondary. Rent would remain
essentially the same even if legislation forbade ail purchase
and sale of land, and land could consequently not acquire any
exchange value ; just as is nowadays the case with labour which,
in contrast with eaiKer times, can no longer be bought or sold
in the form of slave labour.

In this connection, there is another peculiarity which is
common to all, or at least to most, of what we call capital ;
namely, that it is itself a product (‘"produced means of
production ” is a common, and in a sense very good, definition
of capital). Here again, it is contrasted with labour and land ;
or, at any rate, with unskilled labour and virgin soil. Man is
bom, but he is not produced — except in “slave breeding” —
and the sum of natural energy, like the sum of matter, cannot
be either increased or diminished by man.

The above circumstance, together with the indisputable

146 LECTURES ON POLITICAL ECONOMY

fact that capital greatly increases productivity, was long regarded
as a sufficient explanation and defence of interest. Capital
represents, it was said, “ previously-done ” labour (in fact, it
repr^ents, as we shall soon see, not only previously-done ”
labour, but also the previously performed services of the land),
and this, like all other labour, must have its reward ; hence
interest. Thus argued McCulloch, Bastiat, and others. In this
simple manner they believed that they had discovered both
a philosophical and an ethical foundation for the phenomenon
of interest. The latter was especially necessary since, as is well
known, all real interest, at least if it took the form of interest
on borrowed money, was long forbidden in the Catholic, and to
some extent in the Protestant world (though much less objection
was raised, or none at all, to a landowner taking rent, even if
he did not cultivate his land at all).

This explanation, however, is evidently very defective.
The previously-done labour must, of course, have its wages ;
but these wages are not paid from interest, but from capital
itself. If anybody makes a spade, a plane, or any other capital
good, he obtains, by its use, compensation for his work — and
he has no obvious claim to anything more. What is enigmatic
is that the possession of capital, apparently at least, does procure
something more, namely a permanent income in the form of
interest, either without sacrifice of capital or while capital is
constantly being replaced.

It is indeed true that, as a rule, the total product is increased
by the employment of capital, by more (i.e. by a greater quantity
— or value — of product) than corresponds to the capital used up
in production. But this circumstance in itself requires an
explanation. We may, with Bohm-Bawerk, ask why competition
does not either reduce the value of the product or raise the value
of capital goods ^ to such a point that the former exactly
corresponds to the latter, without leaving anything over for
interest. We must not simply take it for granted that capital
can claim the whole of the surplus.

Strictly speaking, capital is necessary for all production ;

^ According to our previous assumption that prices of finished products
are in advance, i e. determined by the world market, the former alternative

should, of course, disappear ; but certainly not the latter, since mtemational
capital transfers are excluded and the pricing of capital goods takes place
in the home market, and must be investigated there.

PRODUCTION AND DISTRIBUTION 147

in its absence tbe product would be more or less negligible.
But can capital on that account claim tbe whole, or tbe greater
part, of the product ? This is impossible ; for, with as much
justification labour could demand the whole — and land also.
There must be a division, but on what principle ? The above
argument gives no answer at aU.

Among earlier writers von Thiinen was certainly the most
advanced in his conception of the nature and origin of interest.
Just as he regarded the addition to the product made by the
“ last worker ’’ as determining wages, so interest was determined
by the ‘‘yield of the last increment of capital”, but he did
not follow out this thesis very far, and, indeed, it is not exactly
correct. Still clearer was the light thrown on the subject by
Jevons in his Theory of Political Economy^ though unfortunately
his theory of capital is still only a fragment of a complete theory.
It was not until Bohm-Bawerk published his great work that we
acquired a theory of the nature and functions of capital, and of
the origin and determination of interest, which, in clearness and
exhaustiveness, satisfies even the most exacting demands. But
in spite of his brilliant style, Bohm-Bawerk’s exposition is marred
by a rather excessive diffuseness ; its wealth of examples is
sometimes confusing to the reader. On the other hand, in my
opinion, his logical analysis of the subject was, in one important
respect, not carried as far as would be desirable from an
expository point of view. I propose, therefore, to present here
Bohm-Bawerk’s principal ideas in an abridged and, if possible,
clearer and more comprehensible form.

B. The Margined Productivity of Cajntah Investment for a Single

Year,

If for the moment we leave aside the question of the origin
of the productivity (or value-creating power) of capital, and
regard it as an empirical fact, we may readily apply to capital
the theory developed above — ^that tiie share of the product
going to any particular factor of production is determined by its
marginal productivity. Actually this is what von Thimenattempted
to do. Just as the additional product of the last worker regulates
wages, so, according to von Thiinen, the rate of interest on aU
capital is regulated by the yield of that portion of capital which

148 LECTURES ON POLITICAL ECONOMY

is Isust employed.^ TMs may seem obvious, for so long as an
entrepreneur obtains a larger return on tbe capital employed in
Ms production than he need pay in interest for borrowed capital
--or can Mmself obtain by lending his own — ^he will, of course,
be inclined to increase his employment of capital. Conversely,
if the interest on borrowed capital is higher than the return on
the capital employed in production, or on the last portion
employed, then he will, as far as possible, curtail Ms employment
of capital to the most necessary purposes or to the more profitable
branches of his production.

Further investigation, however, shows that this analogy
between interest, on the one hand, and wages and rent, on the
other, is incomplete. With labour and land, as we have already
pointed out, the law of marginal productivity applies, with
certain reservations, both to the economy as a whole and to
every private undertaking. If there exists, in any place or
country, a superfluous labourer or an acre of ground wMch
are only capable of making an addition to production less than
that wHch corresponds to the prevailing level of wages or rent,
then wages and rent must tend to fall. (The fact that there
may be a limit below wMch wages physically cannot fall, or on
social grounds, cannot be allowed to fall, is a matter for separate
consideration.) But this theory only applies to capital, as
usually conceived, when we look at it from the point of view
of the individual entrepreneur, to whom wages and rent are
data, determined by the market. If we consider an increase
(or perhaps a decrease) in the total capital of society, then it is
by no means true that the consequent increase (or decrease)
in the total social product would regulate the rate of interest.
In the first instance, new capital competes with the old and
thereby results, in the first place, in a rise of wages and rent,
possibly without causing much change in the technical
composition of the product or the magnitude of the return.
For this reason, interest must certainly fall ; but it need not
fall to zero, or anything like it, even ii the additional product
of the new capital is almost nil. The increase in wages and
rent may absorb the superfluous capital, so that the latter
is now just sufficient for the needs of production, in spite

^ [A mark against this passage in Wicksell’s own copy of the second edition
indicates that he wished to reconsider it.]

PEODUOTION AND DISTRIBUTION 149

of the fact that production has in reality scarcely expanded
at all.

The explanation of this curious divergence is quite simple.
Whereas labour and land are measured each in terms of its own
technical unit (e.g. working days or months, acre per annum)
capital, on the other hand, as we have already shown, is reckoned,
in common parlance, as a sum of exchange value — whether in
money or as an average of products. In other words, each
particular capital-good is measured by a unit extraneous to
itself. However good the practical reasons for this may be,
it is a theoretical anomaly which disturbs the correspondence

The productive contribution of a piece of technical capital,
such as a steam engine, is determined not by its cost but by the
horse-power which it develops, and by the excess or scarcity
of similar machines. If capital also were to be measured in
technical units, the defect would be remedied and the
correspondence would be complete. But, in that case, productive
capital would have to be distributed into as many categories
as there are kinds of tools, machinery, and materials, etc., and
a unified treatment of the role of capital in production would
be impossible. Even then we should only know the yield of the
various objects at a particular moment, but nothing at all about
the value of the goods themselves, which it is necessary to know
in order to calculate the rate of interest, which in equilibrium
is the same on all capital. Again, it is futile to attempt — ^with
Walras and his followers — ^to derive the value of capital-goods
from their own cost of production or reproduction ; for in fact
these costs of production include capital and interest, whereas
our analysis of the laws of the cost of production has hitherto
proceeded on the assumption that production is non-capitalistic.
We should, therefore, be arguing in a circle.

We can, however, escape from this dfficulty if we refer to
the common, or at least similar, origin of the various kinds of
capital. We have already pointed out that capital itself is almost
always a product, a fruit of the co-operation of the two original
factors : labour and land. All capital-goods, however different
they may appear, can always be ultimately resolved into labour
and land ; and the only thing which distinguishes these quantities
of labour and land from those which we have previously considered

160 LECTTJEES ON POLITICAL ECONOMY

is tiaat iiiey belong to earlier years^ whilst we have previously
been concerned only with current labour and land directly
employed in the production of consumption-goods. But this
difference is sufficient to justify the establishment of a special
category of means of production, side by side with labour and
land, under the name of capital ; for, in the interval of time
thus afforded, the accumulated labom and land have been able
to assume forms denied to them in their crude state, by which
they attain a much greater efficiency for a number of productive
purposes — as Bohm-Bawerk, better than any other modem
writer, has analj^ed and demonstrated in such a masterly
manner.

In this circumstance is also to be found the whole explanation
of the value-creating power of capital, or its so-caUed productivity.
What emerges is simply the importance of the time-element
m production. In the real sense, of course, only living human
beings, and seff-perpetuatmg natural forces, especially the sun
and the earth’s physical and chemical forces, are productive ;
only the original factors — ^man and nature. But the productivity
of both becomes, or at any rate may become, greater if they are
employed for more distant ends than if they are employed for
the immediate production of commodities. As has been sa\d,
this increase in efficiency is a necessary condition of interest ;
it is the source from which it flows (just as the fruitfulness of the
earth is the source of rent and the productivity of labour the
source of wages) ; but it does not, on that account, regulate the
rate of interest. Some part of this increase in productivity
accrues, and must accrue, to the other factors of production,
for their co-operation is essential and is indeed itself a part
of the application of capital.

We may thus regard capital as a single coherent mass of
saved-up labour and saved-up land, which is accumulated in
the course of years. The addition of land is of importance ;
English political economy has suffered throughout from over-
looking the fact that one part of capital consists of the saved-up
services of land. John Stuart Mill flatly denied it. And yet
this part of capital is without a doubt as important as the other.
The more elaborate tools and machines noiay owe their existence
principally to human labour ; but domestic animals, raw
materials, and so on, are types of capital-goods which come into

PEODUCTION AND DISTRIBUTION 161

being mainly throngli the resources of the land incorporated
in them. Trees, game, fish, and so on, when wild and mcultivated,
are the sole product of natural forces (if, for a moment, we
abandon the usual terminology and extend the term product to
include also purely natural products). The great majority of
capital-goods consist of saved-up labour and saved-up land in
combination ; but if these two elements are not separable in
reality, we may separate them in theory, as we do in respect
of labour and land as factors of production. In what follows
we shall therefore speak of labour-capital and land-capital as
conceptually distinct elements of the whole mass of physical
capital and we shall mean by them labour and land already
applied — ^if applied by others, bought and paid for: labour
and land which have not yet ripened into finished products —
not present or current labour and land now available,

A special position is occupied, as we have already remarked,
by the stored-up energy derived from earlier periods of vegeta-
tion and found in coal and in ore deposits. They represent, if
anything does, stored up resources of the land of much greater
antiquity than any others employed in production. But since
nobody has owned them from the beginning, they may be treated
economically as stocks of raw material or semi-manufactares
which are spontaneously available. In contrast to the fertility
of the soil, it is largely true to say that these resources may be
used up now, or left unused, according as we desire ; but, on the
other hand, they cannot be renewed. From the latter point of view
they cannot, strictly speaking, be included in the scheme of a
stationary economy.

We have now to consider the stratification of this volxime of
capital through time. Here also, we shall proceed gradually to
our goal ; we shall assume in the first place that, side by side
with the resources of labour and land directly available for the
current year’s production, there exist, in the form of capital-goods,
saved-up resources of the same kind from a single preceding year ;
and that these capital-goods are entirely consumed in the
production of the current year. Naturally, this would bring
about a considerable increase in the total product if the whole
available supplies of current resources in labour and land were
now used in the production of commodities intended for direct
consumption. But, in that case, the advantage will obviously

152 LECTURES ON POLITICAL ECONOMY

be quite transitory and will be obtained only by tbe sacrifices
of the preceding year and by leaidng production in subsequent
years in the same primitive non-capitalistic state as before.
Consequently, we must suppose that a corresponding part of
the resources of the current year is saved in the form of capital
for next year’s production, and so on. As has already been
pointed out, we shall assume stationary conditions as the
foimdation of our observations. This will not prevent us from
considering changes in the quantities concerned, provided that
we do not take into account the actual transition stage, which
is a much more complicated problem, but assume that these
changes have already become final, so that static equilibrium ”
(a stationary state) is again restored. We shall accordingly
assume that the amount of labour and land, saved up in every
year, is always the same. This presupposes a previous adjustment
— ^which we assume to have been made — ^between these two

Year

1929

1928

0

! ^

1

Resources of Labour.

Fio. ii.

1

0

0

1

Resources of Land.

quantities ; for — ^as we shall soon see — ^it may be advantageous,
under given conditions, for the capitalist to save a larger amount
of labour resources and a smaller amount of land resources ; or
vwe versa. As soon as capital has once been formed, then just
as muck labour and land mil go to provide each year's production
and consumption as was originally employed in the non-capitalistic
state. But since a part of these resources has been saved from
the preceding year, in the form of capital, the total product
will, as a rule, be considerably greater than before — at any rate
up to a certain limit ; and it will be greater in proportion as
the part of the resources of labour and land thus employed in
a saved-up form is increased."

This may be more easily understood by means of the above
diagram, which represents production m the current year 1928.
The amount of labour and land employed, either directly or in the
form of capital, for the production of this year’s supply of

PRODUCTION AND DISTRIBUTION 153

commodities is represented by two rectangles, of wMch tbe left-
band divisions (0,0) represent tbe productive r^onroes of tbe year
itself, i.e. tbat portion wbicb is directly employed in tbe course
of tbe year. Tbe rigbt-band divisions (1,1) represent the saved-np
labour and land wbicb are used in consumption this year, and tbe
upper rectangles of tbe same size (0,0) that part of tbe current
year’s resources which are not employed in consumption till
next year.

Tbe dotted rectangles represent partly tbat portion of 1929
resources wbicb, together with those saved up this year, will be
used for tbe direct production of commodities next year, and
partly those portions of tbe productive resources wbicb wil
then be saved up and capitalized for tbe needs of tbe following
year ; and so on.

We shall — as before — assume free competition, at least in
tbe main part of tbe field of production. In such circumstances,
tbe problem' of production will be essentially tbe same as before,
except that tbe factors of production are now increased by two,
namely tbe saved-up resources of labour and land. And it is still
true tbat tbe total contribution of each particular factor of
production cannot be ascertained a priori and does not even exist
analytically. Its share in tbe product must therefore be
determined by something else, and tbat something else is, for
tbe same reason as before, marginal prodiictivity. Now since*
experience shows tbat tbe replacement of a certain quantity
of current labour and land by an equal quantity of stored-up
resources of a similar kind tends in many cases to increase
productivity, and since we assume tbat tbe quantity saved is
only sufficient for use in these cases (and not even for all of
them) it follows that tbe marginal productivity of tbe saved
resources of labour and land is greater than tbat of tbe current
resources — at any rate up to a certain point, not yet actually
reached. This marginal productivity, and tbe share in the
product which it determines, provides in tbe first place,
a recompense for tbe actual capital used up in production, but
it also provides something more. Under stationary conditions
tbe exchange value of goods and services necessarily remains
unchanged year after year, so tbat a person who, in one year,
purchases labour and land in order to convert them into capital,
intended for production in tbe following year, can always count
upon obtaining more product, or value, than be has himself

164 UECTUEES ON POLITICAL ECONOMY

paid out. This surplus is what is called interest. We thus
arrive at the following definition : —

Capital is sami-up labour ard savedrup land. Interest is the
difference between the marginal productivUy of saved-up labour and
land and of current labour and land.

If conditions are not stationary, then of course we have to
take into account changes in the value of similar commodities
(even labour or goods of the same kind) whicb may occur in
tbe course of production — ^and which may easily make the
actual rate of interest earned negative rather than positive.
That, however, is self-evident. Nothmg is more common than
for a large inflow of capital into a certain industry to cause
so great a reduction in the price of the product that capital
is employed for a while at a loss instead of a profit. The real
theoretical difiSculty is rather to explain how, under stationary
conditions, the possession of capital can remain a permanent
source of income. The application to non-stationary conditions
offers no difficulty in principle.

So far as I can see, everything which can be said in
explanation of this phenomenon is said in the italicized passage
above. Of Bohm-Bawerk’s three main grounds why present ’’
goods possess a higher value than future goods (or past goods
higher than present goods), the first refers to the difference
between wants and their satisfaction in the present and in the
future ; the second to the subjective tmdervaluation of future
needs and overvaluation of future supplies. These considerations,
however, are only indirectly significant for the productive
employment of capital. Those who borrow capital for the purpose
of production will not, because of anticipated future suppHes or of
subjective overvaluation, pay more in interest than they actually
obtain themselves by the technical employment of capital.
(They may well be induced in this case to use some of the
borrowed money unproductively for their own consumption
and, to that extent, di min ish the supply of capital and thus
raise the rate of inter^t.)

On the other hand, these considerations play a very
important role in the actual amjimulation of capital ; and in its
converse, the unproductive consumption of capital, as in loans
for consumption purposes. Both logically and for purposes of
exposition it would seem right to begin by examining the effects

PRODUCTION AND DISTRIBUTION 155

of a given supply of capital already accmnnlatedj and then to
inquire tlie causes wMch influence, and eventually alter, tiiis
supply. Thus there remains only the third of Bohm-Bawerk's
mam reasons, namely the technical superiority of the commodities
or means of production available from an earlier stage over those
which will only become available at a later date. Hk reasoning
in this connection essentially coincides with that which we have
already advanced and which we shall develop further ; but it is,
as a comparison will show, considerably more complicated, and
therefore probably not so intelligible as our own. This is
mainly due to the fact that Bohm-Bawerk neglected to base
his argument on the fundamental simplifying assumption of
stationary economic conditions, though he did not really achieve
any greater degree of generality. Moreover, he cannot be entirely
absolved from the charge of trying to prove too much when he
maintains that a ‘‘ present ’’ means of production, e.g. a month's
labour available now, would be, under all circumstances^
technically superior to one available in the future. That, of
course, is not the case. There are a number of cases in which
current labour and land must, from technical necessity, be
employed in their original form and cannot in any way be
replaced by stored-up productive power. But this is not the
point ; it is rather that the margiaal productivity of the latter
is greater, simply because current labour and land exist in relative
abimdance for the purposes for which they can be employed,
whilst saved-up labour and land are not adequate in the same
degree for the many purposes in which they have an advantage.
This again is to be explained by the circumstances which limit
the accumulation of capital.

It is also clear that interest, at any rate within the limits of
the single year’s investment here contemplated, must, according
to our dejGhiition, be the same in all enterprises and all kinds of
employment, and especially that the marginal productivity
(and the share in the product) of saved-up land must stand in
the same relation to that of current land as does saved-up labour
to current labour. Otherwise it would be profitable to save more
labour and less land on the next occasion, or vice versa. We may
remind the reader, in passing, that the technical renewal of
capital from year to year, which is here assumed, by no means
excludes the accumulation and maintenance of capital by the

156 LECTURES ON POLITICAL ECONOMY

indi'wdiml for possibly remote future use. Sucb an individual
need only buy up labour and land in the market in one year
in the form of implements, slaughter animals, etc., sell them
in the following year, and thus repeat the same operation.
In other words, the duration of private capital or, more
correctly, of the ownership of ‘‘^private capital has nothing
to do with the technical period of turnover of social
capital.^

If we assume that the whole of the accumulated capital —
in the form of tools and implements, domestic animals, raw
materials, etc. — consists of A labour years and B acre years, i.e.
of the total production in the last year of A labourers and B acres,
and if I represents wages per labourer and r rent per acre then
the value of capital in money or products will clearly be A . 1 + R . r.
If, in the current year, there are employed in a particular business
a workers and 5 acres of the current year, and labour years
and acre years of the preceding year, turned into capital in one
form or another, then the total product during the year may be
regarded as a function of all these quantities, i.e. F(a, h, bi).

The partial derivatives of this function with respect to each
of the variables wiU be on the one hand, = 1, F^ = r, i.e. wages
and rent for current labour and land, and, on the other hand,
= h(> = ^i( > or what may be called wages

(including interest) for the saved-up labour and rent (including
interest) for the saved-up land, Equihbrium clearly demands
that Zj : 1 : r. The two equal quantities

will then each represent the rate of interest on the investment
of capital for one year. Interest, or that part of the product
which falls to capital, thus equals in the particular business
-h bi.r).z ; and the interest on the total accumulation
of capital will equal (Al + Br)i — on the assumption that, under
free competition, and in equilibrium, all capital will receive
approximately the same return.

A primitive form of the employment of capital mentioned by Aug.
Bondeson in one of his rustic novels, is the communal use of sheep ; i.e. sheep
or other cattle are bought by small rural capitalists or old farm hands and
summer, after which the profit is divided between the owners
of the animals and of the land. In this case the life of the capital^ood is, on
tne average, short, though it does not prevent the prolongation through decades
Of inciividuai capitalistic holdings (and. accumulations).

PRODUCTION AND DISTRIBUTION 157

If we now compare two otherwise similar stationary states,
both investing capital for a single year, but in one of which
there is more capital employed, that is to say, in each year more
labour and land are saved up for the following year than in the
other case, a difficult, but extremely important, qu^tion will
arise ; what influence will the increased emplojnnent of capital
exercise on wages and rent or, in other words, on the share of
the product accruing to labour and land in the current year ?

The fact that their marginal productivity is, normally (as
we have seen) less than that of saved-up labour and land does
not, indeed, prevent it from being increased by the increased
use of capital. This may well appear obvious ; for, in any
particular year, current labour and land participate in the direct
production of commodities in smaller and smaller quantities,
the more the capitalistic method of production is extended ;
and it might be supposed that this would necessarily imply
a relatively increased marginal productivity of those factors of
production. But the matter is not quite so simple. Of course,
ceteris paribus, a relative reduction in the supply of a factor
should cause an increase in its marginal productivity ; and the
increase in the product due to capital would thus accrue in part
to capital, and in part to the other factors of production. But
if the accumulation of capital coincides, as is usually the
case, with technical discoveries and technical progress, it is
quite conceivable that, despite increased employment of capital
and increased production, the marginal productivity and the
distributive share of current labour and land will be Zessmstead of
more. Only in so far as production in given technical conditions
is saturated with capital, is it certain that wages and rent —
usually both — ^will rise, whilst interest falls. Translated into
our terminology, this means that the marginal productivity
of labour and land in the last case gradually increases whilst
the marginal productivity of saved-up labour and land decreases
— so that the difference between them is successively reduced
and may finally disappear altogether ; interest falling to nothing
and the capitalists’ share in the product consisting only of
compensation for the saved-up labour and land employed, i.e.
for the capital itself.

In the following section, we shall apply this conclusion to the
more complex case of capital investment over a period of years.

168

MICTUEES ON POLITICAL ECONOMX

0. CapUal Investment over a Period of Years.

Before aa excess of capital caused interest to fall to notldng,
investment for a single year would in reality have given place,
for the most part, to investment for a period of years. We shall
now examine how this comes about. It is sufficient for our
purposes to suppose labour and land to be saved up for no more
than two years ; investments is thus to be either for one year,
or for two. What we have to say in this connection can easily
be extended to processes of production and capital investment
over any period whatever. We shall also ignore for the present
the period of transition, during which capital is accumulated
for the jBrst time and is suitably distributed over the period
of production in question; we shall only concern ourselves
, with conditions as they are after full equilibrium has been
restored.

Each particular year’s production is now due (1) to current
labour and land, (2) to resources which have been saved and
capitalized during the two preceding years. But on the other
hand, i£ conditions are to remain stationary, two quantities of
labour and land (exactly corresponding to these) must be
withdrawn from the production of consumption goods during
the current year and devoted (1) to production of goods which
will only be used in the following year, (2) to goods which will
only be used in the year after that. Even this does not exhaust
the list of capital goods existing at the moment ; for there
exists at the same time a group of services of labour and land
saved up during the immediately preceding year and intended
for employment only in the production of the next succeeding
year. For this reason, they are to be regarded in the current
year only as items to be carried forward — ^as it were, goods in
transit. (Of course, in reality, the various annual groups of
saved-up labour and land are not always so strictly separable,
but are often combined in the same capitaLgoods — of which
more later.) In the same way, if resources were saved up for
three years, the labour-capital (and land-capital) available at
any moment would fall not merely into 3, but into 3 + 2 -f 1 = 6
distinct groups (cf . the following paragraph) ; and so on, mvJtaiis
mutandis, for more extended capital investments. Thus the
number of capital groups grows, as it were, both in height and

PRODUCTION AND DISTRIBUTION 169

breadtli, or as tlie square of the nimber of years. This, as we
shall see, is a circumstance of great importance.

The following diagrams, which represent the supply of current
and saved“Up labour and land, at the present moment, (1) in
capital investment for one and tw’o years, (2) in capital investment
for one, tw'o, and three years, explain themselves. The figures
1, 2, 3 indicate that the capital groups concerned are 1, 2, or 3
years old, i.e. originate in 1927, 1926, or 1925. By 0 are

Year

Labour.

1930

0

1929

0

1

1928 j

0

1

2

Laud.

Fig, 12.

0

0

1 1

0

1

2 1

represented the current resources of labour and land, whether
used in direct production for the year or saved and capitalized for
the production of succeeding years. The years marked on the left
are to be conceived as representing the year in which the existing
capitalized productive forces on the same horizontal line are
employed for the production of consumption-goods, and this
naturally presupposes that they will co-operate partly with
current labour and land of the same year, and partly with those

Year

1931

0

1930

0

1

0

1

1929

0

1

2

0

I

~ 2 ~

192$ 0

t

2

3

0

1

2

T"

Labour. Land.

Fig. 13.

saved-up and capitalized during preceding years for use in
a future year.

The sum of the rectangles indicated by 1, 1, and 2 (Fig. 12),
or 1, 1, 1, 2, 2, and 3 (Fig. 13) represents the total supply of
capital-goods in existence at the beginning of the present year,
although only a part of them is employed — or, which amounts
to the same thing, is consumed — during the course of the year.
The rectangles one step higher up, identical in size and number.

160 LECTURES ON POLITICAL ECONOMY

indicated by 0, 0, and 1 (Fig. 12), or 0, 0, 0, 1, 1, and 2 (Fig. 13),

represent tbe supply of capital at tbe end of the year.^

If we return to our one-two year capital investment, it is
clear that the labour and capital saved-up for two years will be
remmerated in accordance with its marginal productivity. If we
consider the extremely primitive nature of the implements,
domestic animals, etc., which are possible with investment for
a single year, and the enormous improvement in the technique
of production which would be possible in many fields with
investment for two years, we shall easily see that the marginal
productivity of two-year-old capital must, within very wide
limits, be greater than that of one-year-old capital and a fortiori
than that of current labour and land. But it should be carefully
noted that this does not mean that, in all such cases, investment
for two years would be frojitahle. For that to occur the three
above-mentioned quantities must stand in a certain determinate
relation to each other, corresponding to that which exists in
a calculation with compound interest. In other words, if the
marginal productivity of one-year-old capital (i.e. labour and
land saved-up for one year) is related to that of current resources
as, for example, 1*05 to 1, so that one-year-old capital yields
5 per cent interest, then the marginal productivity of two-year-old
capital must necessarily be related to that of one-year-old capital
at least as 1-05 to 1 ; and consequently to current resources of
labour and land as (1*05)^ to 1, so that two-year-old capital will
yield at hast lOJ per cent interest for its two years. This is
obvious, for otherwise anybody who wished to save capital for two
years or more would prefer to split up the hypothetical two-year
capital investment into two successive one-year investments —
so that the technical period of turnover of capital would still be
only one year.

On the other hand, it may be asked whether the interest
on two-year investments could not be permanently more than
double, say three of four times, that of one-year investments.
A levelling in the opposite direction cannot take place so directly,
since those who desire the return of their capital after the lapse

^ if all the rectangles were of the same size — ^and the co-operation of land
in production were omitted — the above left-hand diagram might serve as an
illustrasion of Eohm-Bawerk’s famous example of a continuous “ staggered ”
production. (Positive Theorie des Kapiials, 3rd edition, book iv, part u I). In
earlier ediiions, book lii, part v.)

PRODUCTION AND DISTRIBUTION

161

of one year have no other choice, it might be supposed, than
a one-year capital investment. But, in an advanced economic
system, credit enters at this point as a levelling factor. So long
as the total amonnt of social capital remains unchanged year
after year (and of course still more if it contimionsly grows),
the technical period of investment is a matter of indifference
to the individual capitalist. As against those persons who, in
the course of the year, desire to call in and consume all or some
of their capital, there would (at least) be an equal number
simultaneously desiring to build up new capital to the same
amount. The transfer of capital from the former to the latter,
and of the corresponding exchange values in money or
consumption goods from the latter to the former, might be
effected by a simple credit operation without the necessity for
the simultaneous liberation of any real capital in the technical
sense. Interest rates for long and short periods do, in reality,
tend to be equal ; the difference which actually exists should
be regarded partly as an increased risk premium for long-term
loans, partly as due to the fact that, under existing economic
conditions, short-term debts on good security are largely used
as cash (money substitutes), a feet with which we cannot here
concern ourselves. Thus, m the supposed circumstances, one-year
capital mvestments in the technical sense would be exchanged
more and more for two-year investments until interest on the
latter became slightly more than double, or, calculated per
annum, as great as the former. If this levelling has been
achieved and full equilibrium restored, it is easy to see that
the surplus marginal productivity of aU the groups of capital
employed during the year, i.e. the total profit on capital of the
year, constitutes one yearns interest on the whole value of the
total capital, each capital group being regarded as representing
the value of the labo^ir and land employed, together with the
ewerued interest. The same naturally applies to longer capital
investments, so that there is complete agreement between theory
and practice.

The whole available capital will now be distributed between
one-year and two-year investment — since, for the moment, we
ignore the possibility of longer dated mvestments — ^and in
a definite proportion ; so that the above relation between the
margmal productivities will obtain. If capital increases, i.e. if

162 LBCTUEIS ON POLITICAL ECONOMY

tlie accumxdated quantities of labour or landj or of botb, are
increased, we may suppose that new capital, and consequently
ultimately the whole volume of capital in existence, will also
be distributed, in the same proportion as the old capital between
these two periods of investment. Yet this does not usually
happen. Such an increase must of itself, in view of what we
have said, and apart from simultaneous technical inventions,
etc., reduce the marginal productivity of saved-up resources and,
at the same time, increase the marginal productivity of current
resources. Excepting for the case where a uniform increase
of both has a specially marked tendency to reduce the marginal
product of resources invested for two years, so that we may
suppose the marginal product of each to fall in about the same
proportion, then it may easily be seen that the relation between
the yields of the two forms of capital will be necessarily disturbed
to the advantage of the longer-term investment ; the interest
on both one-year capital and two-year capital has fallen, but
that on two-year capital is now somewhat more than double
that on one-year (perhaps two and a half to three times as high).
Investment for two years is thus relatively more profitable than
before and extends to fields which it had previously not entered ;
whilst one-year investment expands relatively little, or may
even contract. Thus, in the end, the relative marginal products
of both are brought back to the right relation. In addition to
this, investments for three, four, or five years, etc., which
have previously been unremunerative, in spite of their higher
marginal productivity, now yield a profit and will therefore
be made.

If we represent the marginal productivity of two-year labour
and land by and respectively ; then, in equihbrium, we
must have

^2 : = ^1 : ? = r2 : fi = ri : r.

If we represent this common ratio by 1 -f % then

h = ^(1 -f- h = ^(1 + === about Z(i + 2i),

and similariy for and r 2 . Now if I 2 and are reduced in the
same proportion relatively to I (for example in the ratio 1:1 — e
where € is a proper fraction which is not too small) we obtain

h = ^(I + ^*)(1 — €) or, approximately, = 1{1 + i — e).

PEODUCTION AM) DISTRIBUTION 163
But, on the other hand,

= 1(1 + 2i e) > 1(1 + i - €)K

If, in this case, € > i then one-year capital investment would
show a loss and would certainly be contracted ; if e > 2t, the
two-year investments must also contract and the centre of gravity
of capital investment would shift to longer investments ; and so
on. If, as in the above example, the rate of interest is 5 per cent
per annum, and if, owing to the accumulation of new capital,
the marginal productivity of one- and two-year capital goods
is reduced relatively to that of current labour and land by, say,
1 per cent, then one-year interest will consequently fall to 4 per
cent, but two-year interest to only about 9 per cent instead of
what it should be in equilibrium — ^namely (1*04)® — 1, or
rather more than 8 per cent. Two-year capital investment thus
becomes (absolutely less but) relatively more prohtable than
before. Under certain simplifying assumptions, such as those
made by Bohm-Bawerk and by ourselves in the next chapter
of this work, this fact, which is of fundamental importance for
the whole of the theory of capital, and whose significance was
already recogmzed by Ricardo, can be proved mathematically
as a universal principle.

This has important consequences for the remuneration
of current labour and land, i.e. wages and rent. An increased
investment of capital itself tends, as we have seen, to reduce
the quantities of current labour and land available for each
year’s direct production, and consequently to raise their marginal
productivity. If, however, a relatively larger share of this capital
than before is placed in two-year investments, and the capital
is thus divided into two different parts^ one of which is only
used in the next year, then clearly there will be a reduction, at any
rate relatively, in the quantities of accumulated labour and land
employed each year ; but, at the same time, there wiU also be
a reduction in that part of the current labour and land which
must be saved and capitalized each year to renew that which
is consumed. A larger part will remain over for the current
year’s direct production of consumption goods, whilst, at the
same time, its marginal productivity will fall. It is the peculiarity
of capital that, when it grows, it grows in height as well as in
breadth, and in this there is a counter-weight to the tendency
for an iucrease of capital to raise wages and rents.

Other things being equal, however, this last tendency can

164

LECTURES ON POLITICAL ECONOMY

never be entirely overcome. Inevitably wages and rents (or at any
rate one of them)^ will finally rise — ^tbougb not so much, as one
might at fii^t suppose — ^as a consequence of the increase of
capital as such. But the position is different where, as may easily
happen^ some technical invention renders long-term investment,
even without a simultaneous growth of capital, more profitable
(absolutely) than previously. The consequence must necessarily
be — so long as no further capital is saved — diminution in the
^‘horizontal-dimension’’ and an increase in the “vertical-
dimension”, so that the quantity of capital used in the course of
a year will be reduced ; an increased quantity of current labour
and land will consequently become available for each year’s direct
production ; and, although this need not necessarily cause their
marginal productivity and share m the product to be reduced
— since the total product has simultaneously been increased by
the technical discovery, yet a reduction may clearly result. The
capitalist saver is thus, fundamentally, the friend of labour,
though the techmcal inventor is not infrequently its enemy.
The great inventions by which industry has from time to time
been revolutionized, at first reduced a number of workers to
beggary, as experience shows, whilst causing the profits of the
capitalists to soar. There is no need to explain away this
circumstance by invoking “ economic friction ”, and so on, for
it is in full accord with a rational and consistent theory. But
it is really not capital which should bear the blame ; in
proportion as accumulation continues, these evils must disappear,
interest on capital will fall and wages will rise — ^unless the
labourers on their part simultaneously counteract this result by
a large increase in theif nuTnbers,

That the transformation of circulating into fixed capital,
i.e. the change from short-term to long-term capital investments,
may frequently injure labour is beyond doubt. But Ricardo
was mistaken in his belief that this consequence was due to the
fact that the gross product is simultaneously reduced. This is,
as may easily be proved, theoretically inconceivable. The gross
product under free competition (where such is at all possible)

^ TMs ob^rvation must be made, for capital investment undoubtedly
tends VO disturb the conditions under which labour and land are able to replace
each other at the margin of production. It may therefore happen in exceptional
cases that wag^ alone reap the benefit of a growth of capital, whilst rents fall :
or mce verm, (Cf. also p. 216.)

165

PRODUCTION AND DISTRIBUTION

always tends in tlie main towards tie wiioi it is

piysically possible to obtain witi tie existing means of
prodnction.

In my work, ijher Wert, Kapital uTid Rente (Jena, 1893),
p. 104, I pointed out tie easily-intelligible facs that, if capitalist
employers by common agreement extend tie period of production,
and thereby tie period of capital investment, beyond tie point
consistent witi tieir interests under free competition, tieir
profits will rise, because, witi an unchanged quantity of capital,
wages and rents calculated in money or goods musr neces-
sarily fall.

But, at tie same time, tie annual pyoduct would, up to
a certain point, increase — a fact wiici may appear to confiict
witi tie general principle tiat free competition brings about tie
maximum return from production.

If, however, we regard capital, as we siould do, genetically
(i.e. as tie total of a number of years’ accumulation of labour
and land) tien it is clear tiat, in this ease, there has actually
been an increase in tie volume of social capital — tiat is, an
accumulation of real capital — at tie expense of labourers and
landowners, who do not receive its fruits unless, by co-operation,
they succeed in obtaining better conditions in tie future, by
profit sharing, and so on. A somewhat similar phenomenon
may occur as a result of tie operations of entrepreneurs in
tie money and credit markets — ^as we shall see in tie next
volume.

But tie assumption underlying tie principle outlined above
was tiat all tie factors of production had a given and constant
magnitude and, to this extent, it holds good, even though it
may be difficult — ^if not impossible — ^to define this concept of
social capital witi absolute precision, as a definite quantity.
In reality, it is rather a complex of quantities.

We have now completed the foundation of our static theory
of capital. The complications which we must still take into
account in passing from abstract theory to the concrete
phenomena of reality are not questions of principle, and present
only difficulties of detail in mathematical treatment. The most
important among them is that, on the one hand, labour and land
of different years are incorporated in one and the same capital-
good ; and, on the other, that a capital-good is not, as we have
hitherto assumed, consumed in one year’s (direct) production,

166 LIOTUEES ON POLITICAL ECONOMY

but often serves for many, sometimes for a long succession
of years — so tliat the productive forces embodied in that good
only come into employment successively. What exactly is
consumed in each particular year cannot, as a rule, be
determined. But even in this case, the law of marginal
productivity must be fully satisfied in equilibrium, for otherwise
it would undoubtedly be profitable, at some point in production,
to transfer resources, either by simultaneously decreasing — or
increasing — ^the factors employed at some other point in the
period of production, or by increasing or (hminishing the value
of the capital-good. For example, suppose that a machine has
been constructed in the course of three years and is afterwards
used for twelve years before it becomes necessary to scrap it.
If, in the construction of the machine, an additional quantity
of labour, say one day’s labour, had been added in the jBrst year
of production, then the utility of the machine might possibly
have been increased by, let us say, the value of three consecutive
days’ work during the last year of its use. This day’s labour
would yield an interest of about 8 per cent ; for (1*08)^^ = 3
approximately.

This rate of interest must agree with the rate prevailing
elsewhere, for, if it were higher, it would be profitable (in future
production) to employ more labour on this kind of machinery ;
if it were lower it would be advantageous, in the future, to
content oneself with machines of inferior quality and utility,
which cost less in labour or land for their production.

It is, of course, another matter that some forms of capital
(such as houses, railways, certain forms of improvements of
land, etc.) normally last so long that the quantitative and
qualitative adjustments, theoretically necessary for attaining
equilibrium, become impossible in practice. Unless we wish
to extend our observations over periods of time in which centuries
are mere episodes, we must content ourselves with noting that
there is always a tendency, perhaps very incompletely realized,
working in the direction indicated above. Of especial importance
is the reservation regarding periods of great industrial
development, m which equilibrium is usually conspicuous by
its absence. We shall consider certain questions of this kind in
greater detail in a later section.

PRODUCTION AND DISTRIBUTION

167

Note on Bohm^BawerFs Theory of Intered

What has been said above modifies and completes Bohni'
Bawerk’s theory — a theory which has been the object of more
or less acute criticism by numerous economists. The great
majority of the objections raised are, in my opinion, based entirely
upon misunderstanding or on an inadequate* appreciation of his
reasoning. But some, or rather one, of them does not entirely
lack justification, although, as far as I can see, it by no means
destroys the foundations of his theory. I shall, therefore, give
a brief resume and criticism of Bohm-Bawerk’s theory of interest
as he presented it.^

The first part of his main work, GescMckte und Kritih der
Kafitalzins — Theorien (Capital and Interest), I must omit. In my
opinion, Bohm-Bawerk was entirely successful in showing how
untenable are all the earlier attempts at explanation which
emphasize inadequately, or not at all, the importance of the
time-element in the phenomena of production and value.® With
earlier writers, such as von Thtinen, Senior, and others, who
really do consider this element, it seems to me that Bohm-Bawerk*s
criticism is carried much too far and is sometimes merely hair-
splitting. In particular, I agree with Cassel ® (wMle profoundly
disagreeing with his general opinion of Bohm-Bawerk) that he
scarcely did full justice to Ricardo. However fragmentary
Ricardo’s theory of interest may be, it appears to be quite correct
so far as it goes. Among other things, it contains, in a somewhat
different form, one of the comer stones of Bohm-Bawerk’s own
theory. The passage in Ricardo tp which I refer is to be found
in chapter i, part v, of his Principles^ Ricardo there raises the
question why the employment of labour-saving machinery is
always more profitable with high than with low wages, although
at first sight it might appear as if machinery, being itseK a product
of labour, would rise in price with a rise in wages. With great
acumen Ricardo stows that this cannot be the case : the price
of machinery includes interest as well wages, and if wages as
a whole have risen, then, other things being equal, interest must
fall. (The purchaser who uses the machinery must, for the same
reason, reckon a lower interest on the purchase price of the

1 I have treated this subject in greater detail in an essay in EJconomuh
Tidsknft, 13 (1911), p. 39 et aeq, [Cf. also vol. 16 (1914), p. 322 ci aeg,]

* Before Bohm-Bawerk wrote, Professor Davidson had, in his eaxly
valuable essay on “ De Ekonomiska lagama for Kapitalbildxmgen ” (“ The
Economic Laws of Capital Accumulation”), subjected the so-called “u^
theory ” of Hermann to a criticism, which though brief, essentially corresponds
with that of Bohm-Bawerk, whose fundamental ideas he often anticipates.

* Nature and NeceaaUy of InUrest, 1908.

168 IJmJEES ON POnTICAL ECONOMY

macMnery.) Tiiis is fundamentally the same reasoning as that
with which Bohm-Bawerk proves (as we have done above) that
a rise in wages must lead to a lengthening of the period of
production or of capital investment.

It also follows from what has been said, that a rise in wages
may lead to increased use of machinery for another reason:
machinery is used as a means of replacing labour by land, if rent
has not risen to the same extent as wages.

The second part of Bohm-Bawerk’s work, his Positive Theorie
ies Kapitah, will always retain, its place as one of the finest
achievements of economic theory; but even there he did not
succeed in unifying his theory completely. It seems to rest on
two (or even three) different and imperfectly co-ordinated
foundations.

Already in his Introduction we find the brilliant suggestion
that we should regard the capitalistic process of production (“ the
adoption of wisely-chosen round-about methods ’^) as the
prirmry concept and capital itself as the secondary — the complex
of intermediate products emerging at the various stages of the
round-about process of production taking time This idea,
which renders all further discussion of the nature and content
of the capital concept unnecessary, is subsequently developed
in the masterly book ii, “ On the role of capital in production
and on the accumulation of capital.” The theory is only finally
completed, however, in the chapters on the origin of interest and
the height of the rate of interest — ^particularly in the second
section of the latter chapter, on the determination of the rate
of interest on the market. In these, for the first time in the
literature of economics, a proper account is given of the relation
between wages and interest and, to that extent, a solution is
advanced to the problem of distribution under free competition,
albeit on greatly simplified assumptions and with the deliberate
exclusion of land as a factor of production. ‘ These parts of his
work may be read by themselves, and constitute a complete
whole of the very greatest scientific importance and value. And
yet, here also, Bohm-Bawerk was not entirely consistent, for in
his account of the quantitative factors determining interest he
reverts, probably for reasons of exposition, to the earher Jevonian
conception of capital as a subsistence furid, a sum of (potential)
wages ; so that capital again becomes the primary, and the
capitalistic process of production the derivative, concept.

4th edition) ; Book iy, ohs. 2 and 3 {3rd and

PRODUCTION AND DISTRIBUTION 169

The long section of the hook which lies between these two
portions is of an essentially diSerent character ; and it is this
section which has received by far the most attention from his
critics. After an eshanstrve accotmt — excellent for the purpose
— of modern theories of value and prices (in their Anstrian
form) he proceeds (imder the heading “ Present and Jutnre in
Bconomic Life ”) to his well-known theory of interest in its
widest sense. He here puts forward the doctrine that interest
is originally an exchange phenomenon {and thns no longer
exclusively the resnlt of production and distribution) — is the agio
which arises in the exchange of present against future goods. This
treatment may be justified, in so far as interest is undoubtedly
a broader concept than productive capital itself. It can arise
in a mere exchange of present against future goods or services
without any intervening production and thus without any real
accumulation or employment of capital. But the proof is not
quite convincing. In Bohm-Bawerk’s opinion, the difierenoe
in value between present and future goods which comprises this
agio, originates, like all other exchange values, in their difierent
marginal utilities. But at an earlier stage, Bohm-Bawerk himself
had defined marginal utility as “the significance of the least
significant of the concrete needs or partial needs which are satisfied
by the available supplies of the commodities of the kind in
question ”, and we may add, in full agreement with the whole
trend of his reasoning, “during a given consumption period.”
But if we seek to apply this directly to present and future goods,
the difficulty clearly arises that both the supply (of future goods)
and the period of consumption are quite indeterminate. This
difficulty is not overcome by comparmg, as Bohm-Bawerk some-
times does, present and paM goods. In that case, of course, the
supply of the latter is known (it is the quantity of available
capital-goods), but the period of consumption remains in-
determinate ; for it is far from true that all existing present
and past goods are to be employed in the consumption of the
current year.

Bohm-Bawerk endeavours to circumvent this serious difficulty,
for he clearly asserts that, in all possible cases or, at any rate,
in the great majority (“ in ailer Regel ”) — ^the utility of present
goods is greater ahscdvidy than that of future goods (and less
than that of past goods) of the same kind and quantity ; from
which it must follow that their marginal utihty, and consequently
their value and price, must also be greater. But this position
is evidently untenable. His argument is relatively most successful

170 UECTURES ON POLITICAL ECONOMY

when applied to the seccmd of the three grounds cited as causing
the superiority of present goods, namely the subjective nnder-
valuation of future needs and the overvaluation of future resources
—due to lack of imagination or weak will. This phenomenon
is undoubtedly general, and so long as it exists it creates a
(subjective) over-stress on present goods. But even the first
of the main grounds — ^the existence of an, objectively, more
abundant future satisfaction of needs — ^is evidently ^not general
in its application. The circumstance adduced by Bohm-Bawerk
that those who expect a less abundant satisfaction of their needs
can always hoard existing commodities (especially the precious
metals and other durable goods) cannot, in itself, be a guarantee
of a positive rate of interest, but only implies that interest
cannot fall lower in a negative direction than would correspond
to the risks and costs associated with the storing of these
objects.

Equally unsatisfactory is the treatment of the third main
ground; the technical superiority of present goods — ^including
present agents of production — over future goods. This part of
Bohm-Bawerk’s exposition is, indeed, the one which is most
open to criticism. Proceeding from his general theory of the
profitability of round-about methods of production, he argues
that a certain quantity of present factors of production — ^for
example, a labour-month — ^must inevitably have a greater value
than an equal amount which is available at a future date, say next
year ; the former can be employed as a link in a longer process
of production than the latter and must consequently be more
frmtful, whatefoer foivt in the future is regarded as the final point
of production. This is undoubtedly wrong, for the principle of the
advantage of round-about methods of production by no means
implies that the productive process might be successfully
prolonged for an indefinite time. In order to avoid the absurd
argument that, in such a case, all production might be infinitely
prolonged, Bohm-Bawerk refers to the “ first and second main
ground as bringing the “ economic centre of gravity ” to
a nearer date ; but this is merely a last resort, not to be taken
too seriously. What really limits the length of productive processes
— ^as Bohm-Bawerk himself quite clearly points out later, in book
iii, chapter 5 ^ — ^is not this, but simply the circumstance that
a longer period of production, even if technically more productive,
would yield to entrepreneurs (whether capitalists, labourers, or
u third party), with the available supplies of labour and capital,

[In later editions, bk. iv, ch. 3.]

PEODUCTION AM) DISTRIBUTION 171

a smaller 'profit than the productive processes actually begun.
This has already been shown in the foregoing.

B6hm-Ba work’s real error — ^his cardinal error, as Bortkiewicz
calls it — ^is that at this point in his exposition he seeks to solve
the problem of the existence of interest — ^as distinct from its actual
rate — ^without referring to the market for capital and labour.
This error had already been pointed out by Walras and is, indeed,
the only one of major importance which can be attributed to
Bohm-Bawerk.^

In a subsequent part of his work, Bohm-Bawerk himself
completely rectified this error. It may therefore justly be said
that the work contains, albeit in a somewhat imperfect form,
the real and definitive theory of capital, whereas Walras and his
successors (Pareto, Barone, and others) still continued to hold
a theory of interest which contains both formal and material
defects and which is seriously incomplete. Walras’ formula for
interest, as may easily be seen (cf. the preface to the second and
subsequent editions of his Elements d^economie politique pure)
reduces itself, on the assumption of stationary conditions, simply
to the equation E{i) = 0, in which F{i) is the amount of annual
savings conceived as a function of the rate of interest i. In other
words, it expresses the truism that, in the stationary state, the
inducement to new savings must have ceased ; but it afiords
no answer to the question why a given amoimt of existing social
capital gives rise to a certain rate of interest, neither higher nor
lower. The importance of the time-element in production was
never properly appreciated by Walras and his school. The idea
of a period of production or of capital-investment does not, as
we have said, exist in the Walras-Pareto theory ; in it capital
and interest rank equally with land and rent ,* in other words,
it remains a theory of production under essentially non-capitalistic
conditions, even though the existence of durable, but apparently
indestructible instruments, is taken into account. In the same
way, Barone, who, in the essays in the Giornale degU Economisti
cited above, approached the views of Bohm-Bawerk, appears,
from a later essay in the same journal, to have reverted to the
earlier unsatisfactory point of view.*

^ There is, however, no question of an error in Bohm-Bawcrk’s theory
of capital, but in my opinion only of a lack of clearness in exposition, for
which reason I do not tlnnk it necessary to examine his reply to Bortkiewicz,
bo whose criticism as a whole I cannot subscribe.

* [Cf. Wicksell’s article Zur Zinstheorie {Bdhm-Bawerks DrUter Qntnd)
in Die Wirtachaftstheorie der 'herausgegehm von Hans Mayer, iii,
199-209 (1928), The manuscript was copied and despatched soon aft^ the
author’s death.]

172 LEOTUEES ON POLITICAL ECONOMY

D. An Alternative Treatment of the Problems of Interest and

Distribution.

The following method of considering interest is designed
to bring out the importance of the time-element, which is the
real kernel of the capital concept.

Let us begin with the simplest conceivable case of the
employment of capital; this undoubtedly occurs in that
form of production where the original factors, land or labour
(or both), are used only once, as it were in an indivisible moment
of time, after which their fruits are spontaneously matured by
free natural forces. A concrete example of this kind (at any rate
approximately) is to be found in the laying down of wine for
consumption — a copybook example rightly favoured by
economists ; or alternatively in the planting of trees on barren
land (where no question of rent need enter during the period
of growth) and so on. In such cases, the function of capital
is merely to preserve, for a longer or shorter period, the services
of the labour and land in question ; or, where hired labour or
land is used, to advance wages or rent for the corresponding
period. If the total supply of labour and land is given, the
length of time will thus be the only variable dinhension of capital.
If, in such a simple case, we are able to deduce the general laws
of capital and interest, this deduction may be regarded as an
essential ingredient in the explanation of all the more complex
phenomena of actual employment of capital.

Let us imagine a country or district which, as far as its
land, labour, and capital are concerned, is a closed economy
and which by reason of the nature of the land and climatic
conditions, produces only a single commodity— let us say
a certain kind of wine — ^in exchange for which it obtains all
other commodities from neighbouring countries or districts.

Let us farther suppose the price of the matured wine to be
determined in advance on the market in such a way that, within
certain limits (not reached in practice) it increases continuously
with the age of the wine. The annual vintage, say one million
hectolitres, we regard as the product of land and labour only ;
and for the sake of simpKcity we ignore the capital employed
in the viniculture itself — ^though in practice this is very important.
The price of the grape juice Yq (per hi.) may thus be entirely

173

PRODUCTION AND DISTRIBUTION

resolved into wages and rent. How it will be divided between
theni (since we ignore tlie labour required in later stages) is
a problen^ of exactly the same kind as we have considered 'in
the previous section (ii, 1) and with which we need not further
concern ourselves. We might even assume, without violence
to the general applicability of our principle, that the whole
value of the raw product consists of wages only, by assuming
that the use of the land is free.

The price Vq is still an unknown quantity and must be
carefully distinguished from the price which the new wine
would command if it were now offered for consumption. But
we shall assume that the latter alternative is not in question,
as it would be too uneconomical. Rather the whole vintage
will be stored, either by the producers or by other entreprenem^,
for a number of years — in order that it may be sold to greater
advantage. How long it will be stored depends, as we shall soon
see, exclusively upon the amount of the existing capital, which,
on our assumption of a closed economy, can neither be increased
by additions from outside nor diminished by export. The whole
of the circulating capital of that society will consist of stored
wine, though it can at any time be wholly or partially converted
into money ; we still make no deiSnite assumption about the
value of this capital in terms of money, but we assume that it
just suffices for each year’s vintage to be stored for a particular
period (say four years).

In that case, a rule, the 4-year storage period must
be the one which is the most profitable from the point of view
of the individual vine growers. For if, at the current price of
grape juice, or, in other words, at the current rate of wages (or
wages and rent combined), a 5-year storage period would be
more profitable (would yield a higher rate of interest) it would
be preferred by some or all owners of the wine ; but since the
total capital is not sufficient for that, the consequence would be
that at subsequent harvests a smaller amount of money would
be available for the purchase of grape juice, so that the price of
grape juice, and consequently wages and rents, would fall. If,
however, the price of the new wine was lower (as our arithmetical
example below will show) it can easily be proved that a shorter
storage period would be more profitable than the one which
had previously yielded the best return.

174

LECTURES ON POLITICAL ECONOMY

Again, if the price of new wine (on the home market) were
so low that a storage period of only three years was the most
profitable from the individnal point of view, then, on our
assumption, there would now be an excess of capital, so that
more than the sum previously available each year from sales
would be devoted to the purchase of new wine. The price of
new wine would thus rise, and the storage period most profitable
from the individual point of view would become longer.
Equilibrium therefore requires an equal storage period for all
— and a period of such length that the whole of the capital in
existence finds employment in the only productive use which
is open to it on our assumption — ^the storing of wine. All this
is true as a general rule. We shall later consider a not unimportant
exception (though it is more apparent than real).

We now further assume that the price of the matured wine,
which is definitely fixed in the world market, is such that, when
sold for consumption abroad, 3-year wine commands a wholesale
price of 90^. per hi., 4-year wine IOO 5 ., and 5-year wine IIO 5 .

We have now all the data which are necessary to determine
(approximately) the unknowns of the problem, which are : —

(1) The equilibrium rate of interest in the community.

(2) The price of grape juice, or what comes to the same
thing, the sum of wages plus rent (the division between these
two, as we have said, being each determined by the law of
marginal productivity in the non-capitahstic production of
new wine, which we have postulated),

(3) The amount of capital in the community, reckoned in
terms of money.

First of all, it is evident that the equilibrium rate of interest
must be greater than 10 per cent, since 6-year storing would
otherwise be at least as profitable as , 4-year — ^if not more so ;
for the conversion of 4-year wine, with a selling value of lOO*'.,
into 5-year, with a selling value of 110a., would yield interest
at exactly 10 per cent per annum.

In the same way, the prevailing rate must necessarily be
less than 11 per cent (or to be exact, less than 11-11 per cent),
for it would otherwise be equally profitable, or more profitable,
to sell out the wine after three years ; for the mayirmiTY^ rate
which can be obtained by leaving the wine for another year is

PEODUCTION AND DISTRIBUTION

175

about 11 per cent on its price at that time of 9ft?. (it® price
after four years being 100^.). The actual rate of interest must,
therefore, lie between these two limits — say at 10| per cent ;
for a more exact determination we should have to know the
selling value of the wine when it was between three and four and
between four and five years old.

The rate of interest being known, it is easy to solve the
rest of the problem. It is clear, for example, that the price of
the 3-year wine in transactions between holders themselves (which
we may call Fg) must be such that, when capitalized for one
year at the current rate, it equals the selling price of the 4-year
wine. In other words, we obtain the following equation : —

Fg = (M05)’i X 100s. (per hi.).

This price, which we may call the capital value of the
3-year wine, is, as calculation shows, a little more than the
905. which the wine would have fetched if sold for consumption,
which agrees with the fact that, in those circumstances, such
a sale would not be profitable. In the same way, the capital value
of the 2-year wine must be (I-IOS)”*^ X IOO 5 ., and that of
1-year wine (1*105)“*® X IOO 5 ., and, ^ally, the O-year wine
or new wine in the home market must fetch an amount
represented by the equation : —

Fo = (1*105)-^ X 100 = 675. (per hi.)

This will therefore be the sum paid out in wages (and rent)
for the production of 1 hi. of new wine. The total wages and
rent per annum will consequently be 67,000,0005.

Apart from the supply of cash to effect transactions and
certain other requisites, the circulating capital of the community
— ^as we have already said — consists entirely of the stored wine
of four successive vintages. Consequently, its money value at
the beginning of each year of account, when the mature wine
has been sold, or exchanged for commodities from abroad, and
a new vintage has just been laid down is : —

= [(1*105)"*^ -f {1-my^ + (1*105)“® + (1*105)“1]

X 100 million shillings, or, what amoxmts to the same thing : —

67 miffion shillings x [1 + 1-105 -f (1-105)® + (1-105)®] =
67 — ~ million shillings = 314 million shillings.

176

LECTUEES ON POLITICAL ECONOMY

At tlie end of a year of acconat, shortly before the next sale,
the whole stock of wine has become a year older. Its value
has thus increased to

{1-105)5 -1-105

8i ^ — = 347 million shiliings.

0-105

The diSerence between th^e amounts, 33 million shiliings, is the
lemoneration of capital for the year, and may clearly be regarded
either as four years’ interest on the purchase price of new wine, i.e.

67 [(1-105)^ - 1] = 100 - 67 = 33 milHon shillings,

or as one year’s interest on the whole of the capital existing
at the beginning of the year, i.e.

314 X 10|^% = 33 approximately.

Now if, by continued saving, the capital of the community
is increased so that it just suffices for 5-year storing, then (with
the same reservations which we shall discuss in detail later)
this storage period must necessarily be the most profitable
from the individual point of view. In order to calculate the
approximate rate of interest under such conditions we must also
know the selling price of 6-year wine, which we will assume to
be 120«. per LI. in equilibrium the rate of interest must then

be less than 10 per cent, but more than (about 9 per cent).

We wili assume it to be exactly per cent. The price of new
wine must consequently be Fo = 110 x (i-095)~5 =69*88 or
70^. nearly. Thus wages and rent will now amount to nearly
70 million shillings. The remuneration of capital will thus be just
over 40 million shillings per annum and the commiinity’s total
capital at the beginning of each year of account : —

This considerable increase in capital has thus somewhat
increased wages plus rent, whilst at the same time lowering
the rate of interest. Nevertheless, the share of capital in the
annual product has increased^ since 40 : 70 > 33 : 67 — relation
which, with a continued increase of capital, must finally be
reversed, so that the relative, and ultimately the absolute, share

PRODUCTION AND DISTRIBUTION 177

of capital in the product will be deareasei when capital has
increased sufficiently.

The rate of interest here appears clearly in its simplest
form as the marginal 'productmty of waiting By prolonging
the period of storage (i.e. the period of production or capital
investment, which here coincide) by one year — ^from four to
five years — ^the annual product has been increased from 100 to
110 million shillings, or 10 per cent ; if it were prolonged yet
another year it would increase from 110 to 120 milli on shillings,
or about 9 per cent. Between these two Kes the real rate of
interest for exactly five years’ storage.

On the other hand, we find from this reasoning that von
Thiinen’s doctrine of the determination of the rate of interest by
the yield of the last portion of capital applied, gives, when taken
with reference to the whole capital of the community — ^reckoned
in money (or consumption goods) — ^too low a value. Capital was
increased by 422 — 314 = 108 miUion shillings and gave rise
to an increased annual yield of 10 million shillings, which, on
that basis of calculation, would correspond to a rate of not quite
per cent. A further increase of capital, bringing the period
of production up to six years, would in the nature of things
produce a still smaller increase in the relative yield ; and between
these two lies the yield of the last portion of capital when the
period of production is exactly five years. Thus it is in any case
l^s than 9|r per cent, on which basis we have calculated the money
value of capital. This relation appears to be general, and the
difference may be of any magnitude whatever.

In the example here selected it may, of course, easily happen
that the capital of the community may become too great for
4--year storage and yet not great enough for 5-year. In that
case, wages (the price of new wine) wiU simply rise until 4-year
and 5-year storing are equally profitable, and capital is
distributed between them. But it might also happen that one or
more vintages (e.g. 5- or 6-year wine), although more valuable
than new’er wine, may fetch a market price relatively so low that
it does not pay to sell for consumption wines of these ages.
As capital increases, the storage period will then rise in
discontinuous jumps from four to seven years. This is the
exception to the rule, which we have already mentioned.

In fact, such cases are not infrequent. In the same industry

178 LECTUEES ON POLITICAL ECONOMY

(it happens in shoe manufacture in Sweden) there may exist
side by side two or more methods of manufacture, perhaps
requiring entirely different amounts of capital and with different
pr^uction periods (e.g. hand-made and machine-made shoes).
Only in proportion as capital (and with it wages) increases will
long-period capital investment finally supplant short-period
investment (except possibly for certain specialities).

We refer the reader to the following pages for a more exact
deduction of the above principles, as weU as for a treatment
of the more general case in which the application of labour and
land is not (as we have here assumed) simultaneous, but made
at different times.

In an algebraical treatment it is simplest to start with
a coTdinuom production and sale ; that is, the production of so
many hectolitres of grape juice per day and the sale of an equal
amount of matured wine every day, on the assumption that these
two operations are separated in time by a period of i (years).

If we again represent the price of one hectolitre of grape juice
as Fo and the price of the mature wine, treated as a function of
its age, as TFf or TF (as distinct from Yt by which, as before, we
represent the capital value in the home market of wine t years
old), we shall clearly have

i^=/{o = n(i+*)',

in which i is the rate of interest ; or, as it is more convenient
to write it

W = Y^ept (i)

in which e { = 2*718) is the base of natural logarithms and p the
rate of interest at a moment of time (Yerzinsungsenergie). The
individual capitalist cultivator has now, with a given value of
Fo, to maximize i or, what comes to the same thmg, p. This
requires that

W'

p-w ( 2 )

where Tf ' represents the first derivative of TF with respect to
t. This is Jevons’ well-known formula for interest : “ the rate
of increase of the produce divided by the whole produce.”

The further condition for a maximization of p can be
written : —

IF, W'

W\ TF"

<0

(3)

PRODUCTION AND DISTRIBUTION 179

where W is the second derivative of If with respect to L This
may also be written : —

If ' : If > If ^ ; If',

and it is consequently always satisfied if If increases less than
geometrically when t increases arithmetically ; this must always
be the case in the long run, since the contrary assumption would
lead to absurd consequences, though it need not, of course, hold
for every value of L

By the ehmination of p between (1) and (2), we obtain the
value of t which maximizes p for the given value F©. If, instead,
we had assumed the value of p to be known, then the sarn^
formulae would have given the value of t which maximizes Fq,
i.e. the storage period which the cultivators themselves would
adopt, if they could borrow money at the rate of interest p for
their current expenses.

Let us now assume that the capital of the community is just
sufficient for a storage period of t jea.Ts — i being assumed to be
known. The equations then give us the values of Fq and p,
which correspond, when the community is in equihbrium, to
wages (or wages plus rent) and the rate of interest .

If the grape harvest comes in once a year and if Fq is the
total value of this annual harvest, If^ having a corresponding
significance, then the money value of the social capital wiH
clearly be : —

Fo.^(i+*r=-- - - -

a- an 0

On the other hand, with production, storage and sale, all going
on continuously, the result wiH be : —

If the social capital is exactly equal to this there will be
equilibrium. If it is greater or less, the equilibrium will be
disturbed ; the value of F^ will rise or fall and the storage period
most advantageous from the individual point of view will be
altered,' until a new equilibrium is reached. It is clear that, with
an increase in K, there must be an increase in Fo> in i, and in
IT, but a fall in p. By logarithmic diSerentiation of (I) and
applying (2) we obtain ; —

SFo

1^0

= — thp = —

F,]F'

ir,F"

w

tht

( 5 )

180 LECTURES ON POLITICAL ECONOMY

and since the determinant in the last expression is assumed
to he negative SFo and will clearly have the same sign, while
SFq and Sp, as well as ht and Sp, will have opposite signs. That
ZK and hi must have the same signs, is inherent in the nature
of the case, but can easily be directly proved. By diferentiating
(4) With the help of (5) we obtain : —

hK = P ~ Po(l +

Since, in accordance with the above, p^ is always negative and
1F= > Vq(1 + coefficient of St clearly >0 so

long as IF increases with t

In the same way we obtain ; —

Now since dp : dK is always negative and K is always >
(from (4) since the function under the integral sign is always
> 1 so long as /} > 0), clearly dW : dK is always less than p.
This proves that the above-mentioned theorem of von Thiinen
is not coraect, if by “the last portion of capital” is meant an
increase in the social capital. The divergence may in point of
fact be of any magnitude whatever, since K — V^t, and
also dp : dK may have any values whatever.

If we desire to represent these conclusions graphically.
It IS simplest to take the natural logarithm of the productivity
fimction, y = = loge (IF<) as the ordinate of a curve whose

a^iBsa is the time t. Similarly we take Wg, i.e. the fixed price
OT new wine on the world market (as distinct from the variable
Kj) as a unit for measuring Wf, so that log If o = 0.

The curve must then pass through the origm.

PRODUCTION AND DISTREBUTION

181

If logj (F(,) is called y^, then for any value of t, p=z so

tKat p becomes the trigonometric tangent of tbe angle of inclination
of a straight line connecting the point on the ^-axis with
the corresponding point on the curve y s= = log^ {W^
and p will be. a maximum when this line becomes a tmymi to the
curve. In accordance with what has been said, the curve must be
roughly parabolic — ^i.e. it must be concave to the i-axis, since
a rise in y^ and t always leads to a fall in p. If, in exceptional
cases, the curve should at some point bend downwards, then
this point will be bridged over by a double tangent to the curve ;
capital will be divided between two equally profitable periods
of investnient (or production) and di&rent in length ; while
p and Vq remain unchanged until the community’s capital
increases to such an extent that it more than suffices for the
whole of investment to be made for a period ig, after which Vq
will again begin to rise and p to fall.

We may consider briefly the somewhat commoner case in
which labour and land are still employed, once and for aU, in
what is practically an indivisible moment of time, but when
they are employed at difEerent points of time, during the period
before the completion of the commodity ; as for example it would
happen if the grapes themselves were a spontaneous gift of nature,
for which no appreciable wages, though some rent, need be paid,
and the actual labour is employed in the making of the wine at
a later time not definitely predetermined. In an individual firm, the
value W of the finished product available during a given unit of
time (say one year) would clearly be a function of the quantities
of labour and land employed (a and. 6) and also of the periods of
time {t and r) for which each was invested in production : —

W =f(a, 6 , t, t ).

Out of this value W must be paid wages, rent, and accumulated
interest. If I represents wages and r rent we thus obtain : —

W ^f{a, 6, t, t) = a.l.eP^ + b.r.ef^ (1)

where e and p have the same significance as before. If p is to
be maximized, we can difierentiate partially (1) keeping p
constant. By partial differentiation of (1) we then obtain : —

ft, = rep^ ( 3 )

/* = paleP^ W

fr = pbreP^ (5)

182 LECTURES ON POLITICAL ECONOMY

From these five equations the unknowns a, h, t, r, and p can
generally be determined. From (2) and (3) we readily obtain : —

®/a + ¥b =/( ) = W.

This equation, however, is an identity so long as TF =/( )
is a homogeneous and linear function in a and b and is thus of the

form b.F(^y ty ; in other words, if large and small-scale production

(at any rate after a productive capacity, which is not too great,
has been reached) are equally profitable.^ In that case the number
of independent equations is reduced to four, but we can still
determine t, r, and p as well as the ratios between a and b since
(1), when divided by b, gives ; —

( ct \ a

t, Tj -leP* + reP'f'.

If the whole production of the community is of one and
the same kind we may, on the above assumption, simply replace
a and b by the total annual services of labour and land (A and
B). These, however, are to be regarded as given and constant ;
but the above five equations (1) . . . (5) can, after this
substitution, serve for the determination of I and r (as well as
t, T, and p). Since, however, only four of them are independent,
a further equation is required, which may be obtained either by
supposing t or r (or some particular relation between them) to be
given, or else by some supposition as to the money value of the
social capital, which in this case will be equal to the sum of
t years’ wages and r years’ rent plus interest accruing at the
rate of p (or i).

From (4) and (6) we clearly obtain, by addition.

P =

ft +/t
/( )’

which corresponds with the above-mentioned formula of Jevons
and, on special assumptions, coincides with it.^

In the same way it is easy to see the significance of equations
(2) and (3). The partial derivatives with respect to a and b (or
A and B) no longer correspond (as in the case of non-capitalistic
production) to the actual wages and rent paid, but rather to
the amount which labourers and landowners would receive, if

^ rWicksell’s notes indicate an intention to re-write this passage.]

It does so if ly =:/( ) is a function of only (as well as of a and
6) and if t and r should happen to be equal.

PRODUCTION AND DISTRIBUTION 183

they could wait until their product was finished ; which must
otherwise be discounted at the rate p for the period t or r.

At this point we cannot enter into a detailed discussion of
these formulae. We have already remarked that an increase in
capital need not in this case necessarily lead to an increase in
both wages and rent ; one may sometimes remain stationary,
or even decline, whilst the other correspondingly increases when
capital is increased, and vice versa. On the other hand, it appears
inconceivable a priori that an increase of capital could, ceteris
paribus^ coincide with a decrease of both wages and rent — ^though
the question should perhaps be further investigated.

We must now try to solve the problem of production and
distribution in the general case, where the original factors are
employed not merely at one or more discreet points of time, but
are distributed over the whole period of production. This
distribution — ^which varies within very wide limits — ^is only
partly determined by the technique of the difEerent industries —
and is actually modified in the effort to maximke profit.

It is evident that the solution would be impossible, even
from a purely mathematical point of view, if it necessitated
a precise treatment of the production and distribution of the
community as a whole. But the only questions of practical
importance which economists have to answer relate rather to
the recurrent, relatively small, changes in a scheme of production,
the elements of which are known from experience ; and of
foreseeing the probable effects of such changes on production and
distribution, within the community. (Even the revolution which
would follow the introduction of the socialist state would
probably only be relevant to the question of the ownership
of the means of production, with which we are hot concerned
here ; it might affect the technico-economic side of production
and distribution to a much smaller degree.) ^

Even with this reservation, the problem must probably
be regarded as incapable of solution at present — chiefly owing
to the lack of reliable industrial statistics. On the other hand,
the mathematical aspect should not present any insurmountable
difficulties once the principle is established.

The problem is considerably simplified if the period of
production, or the rate of interest, or both, are so small that we

^ [A pencil mark against the last lines indicates that this observation
is made with reservations.]

184 LECTUEES ON POLITICAI. ECONOMY

can use simple interest without risk of serious error (as Bohm-
Bawerk does in his illustrations). In such circumstances the
average investment-period of both labour- and land-capital will
be indefendent of the rate of interest and will simply be equal
to the (weighted) arithmetic mean of the individual periods
of investment. We may then regard the productivity function
/{ ) as merely a function of these two average investment-
periods t and T (as well as of a and h or A and B) and everything
can be reduced to the simple formula on p. 181, in which the
exponential functions on the right-hand side of the equation are
replaced by the expressions 1 + i.t and 1 +

This is not without practical importance, since in a more or less
stationary society — as we shall proceed to show — one can
completely ignore the longer periods of investment ; for capital-
goods already- in existence (such as houses, railways, etc.) will
stand in a similar relation to circulating capital , and labour
as land itself. The investment period of circulating capital,
therefore, is reduced to a few years, and it will thus be sufficient
to employ simple interest in its capitalization. The line of
demarcation between fixed and - circulating capital must, of
course, be drawn more or less arbitrarily, but in such questions
we can never achieve more than approximately valid conclusions.

It should perhaps be pointed out here that the assumption
that the average period of investment is independent of the rate
of interest (i.e. of simple interest) only applies, strictly speaking,
where several different capital investments relate to one and the
same future act of consumption (as in Bohm-Bawerk’s example).
In the opposite case, where one (or more) factors of production
are invested in a single capital-good or durable consumption-good,
it may easily be seen that the average investment-period will
be dependent on the rate of interest, even with simple
interest.

On the whole, the theory of the coincidence of the rate of
interest and the “ maiginal productivity of waiting ” is only
applicable as an exact mathematical formula on certain abstract
assumptions. This is quite natural, for waiting on the part of
society as a whole — and frequently also on the part of the
individual— is not a simple quantity, but is, as we have just
pointed out, a complex; ‘‘average waiting as a rule exists
only as a mathematical concept, without direct physical or
psychic significance. But it should, nevertheless, be retained
as a concise general principle, reflecting the essence of productive
capital.

PRODUCTION AND DISTRIBUTION

185

E. Controversies Concerning the Theory of CapituL

Before proceeding, we may turn to consider, in tlie light of
the theory we have now developed, some of the controversies
concerning capital which have for a long time past engaged, and
are still engaging, the attention of economists. If we succeed
in throwing new and clearer light on these questions, this will
be the best proof that the new theory really makes some scientific
progress. In this case — as in so many others — a closer examination
will show that the difficulty is, to a large extent, purely formal,
and is due only to an imperfect formulation of the point at issue.

(1) This is probably true of most questions concerning the
content of the capital concept itself, and especially of the
question whether or not land should be included under the
designation of capital. There is no doubt that we can give to
the word capital a meaning wide enough to include land also.
Here, as in practically all economic definitions, we are concerned
with a more or less conscious extension of a concept whose
meaning was originally more restricted. Such an extension
can be taken as far as we like in view of the question in hand
— ^nothing in principle need be excluded. If we contrast capital
(as being equivalent to material means of production) with labour,
then of course it also includes land. One might, though the
practice is unusual, go further and, with Walras and Pareto,
consider man himself (human sMU and ability) as capital. The
latter concept will then be equivalent to the sources of productive
power in general, or, from another point of view, to the concept
of a source of income, of any kmd, in contrast with income itself.
There is nothing to prevent us from speaking of capital in the
wider sense ’’ as well as of capital in the narrower sense
so long as no misconception arises. We believe, however, that
we have already given good reasons for the tripartite division
of the factors of production into land, labour, and capital, which
is commonest among economists. The almost complete analogy
between land and labour, from an economic point of view —
which has so long been overlooked by economic science — appears
very clearly from the modem theory of marginal productivity ;
in contrast with these two original, current, present or direct
productive forces, capital appears as a combination of accumulated
labour and land.

186

LECTURES ON POLITICAL ECONOMY

It is admittedly difficult to determiae where the line is to
be drawn between capital and non-capital, indirect and direct
productive forces. The human labour employed on land, and the
resources ofthe land accumulated from earlier ages and employed
for the same purpose (e.g. the work of beasts of burden in
improving the land ; manure ; timber for roads ; agricultural
and other buildings, etc.) are undoubtedly to be regarded as
capital, when the measures and expenditures in question are
taken in order to yield interest at a future date — ^as in the case
of all other capital. Such improvements to the land often leave
a permanent residual benefit. This happens, for example, in the
case of major blasting operations to secure water in mountain
regions, the building of roads, protective afforestation, etc.
These new qualities which, once acquired, the land retains for
all posterity, cannot of course be distinguished either physically
or economically from the original powers of the soil ; in the
future they are to be regarded not as capital, but as lard. Very
much the same applies, moreover, to human skill : a manufacturer
who enlists skilled foreign labour in order to introduce a new
industry into the country makes a capital investment which
may perhaps repay him to the full in a few years. But the
skill in this industry, which perpetuates itself within the country,
will be a future asset for labour and not for capital.

It may be further pointed out that nearly all long-term
capital investments, nearly all so-caUed fixed capital (houses,
buildings, durable machinery, etc.) are, economically speaking,
on the border line between capital in the strict sense and land.
We have already said that the operation of the laws of capital
depends upon the assumption of a constant adjustment of
concrete capital goods in an endless repetition of the same
process of investment and production. But this is only of practical
importance in capital investments of relatively short duration.

If, therefore, our analysis is only applicable within a fairly
short period, then, strictly speaking, only short period capital-
goods (in other words, circulating capital) can be regarded as
capital proper. The volume of fixed capital, on the other hand,
can, in the long run, be increased by the conversion of circulating
into fixed capital — ^in so far as this is generally profitable — but
it cannot be appreciably diminished — ^the reverse operation
being usually impossible. Hence it is, in most respects, on the

PRODUCTION AND DISTRIBUTION

187

same level as the michanging original productive factors, labour
and land. This circumstance is sometimes in evidence during
booms, when large quantities of circulating capital are converted
into fixed capital, and it is not possible to replace the former
quickly enough. In the subsequent depression the conditions
are usually reversed : there is plenty of circulating capital,
but it is no longer profitable to convert it into fixed capital.

(2) Similarly, the question of the inclusion of necessities
of life for the labourers within productive capital is — ^at least in
part — of merely formal importance. They have long been
considered as a part of circulating capital ; while Jevons
considered that, fundamentally, all capital — especially in its
original free form — consisted of the means of subsistence. In
apparent opposition stands Bohm-Bawerk, who would entirely
exclude such commodities from productive or social capital ; for,
in his view, the latter consists rather of the sum of the
intermediaie products appearing in the course of production and
right up to the final stages — ^whereas the labourers’ means of
subsistence are finished products and direct objects of
consumption. It might be thought that this almost direct
contradiction indicated a deep-seated difference in the capital
concepts of the two writers. Yet they are fundamentally in
agreement and both may be described as thorough-going
representatives of the modem theory of capital. The whole
controversy is, in reality, merely formal ; if we regard the
selling process as a stage in production, the finished products
may also be regarded as intermediate products, in the technical
sense, until they pass into the hands of the consumer. Since,
in our day, almost all labour — at any rate in industry — ^is hired
labour, the means of subsistence, in proportion as they are
consumed by the labourers (in other words real wages) may be
regarded as the price of the labour which the capitalist acquires
in their stead, and which he adds to his stock of capital-goods,
in the form of saved-up labour of one kind or another. The cases
in which the labourers themselves are entrepreneurs may be
regarded in a similar way — ^the labourer’s wages being considered
as a quantity of goods equal to that which he would obtain
in the market if he hired out his labour. If we look at the
problem in this way, there is no real difference between the views
of Jevons and Bohm-Bawerk.

188 LECTURES ON POLITICAL ECONOMY

The fact that Jevons’ definition of capital is too narrow,
since he proposes to reduce it merely to labour and its means
of subsistence, is quite another matter. In so doing, he takes
account of only one part — ^though usually the larger part — of
capital ; whereas in reality another part, and certainly a very
important part, consists not of saved-up labour but of saved-up
land — ^not of wages advanced but of rent advanced. But this
part — ^which cannot be physically separated from the other —
permits, as we have seen, of exactly the same treatment.

Hence, when Bohm-Bawerk observes, in support of his case,
that if labour’s means of subsistence are reckoned as capital
the consumption-goods of landowners and capitalists must also
be so reckoned, the first part of this observation (concerning
landowners) is undoubtedly true. The capitalists’ means of
subsistence evidently constitute a part, not of capital, but of
the interest on capital. Nor are they advanced — ^for who could
advance to the capitalist ? On the contrary, they are obtained
subsequently, when the production of commodities, with the help
of capital, is concluded,^

(3) Of more real substance is the dispute, which still
continues, whether capital is really the source of wages or whether
the source is not rather to be found in the annual product —
in the results of production. The former is the classical view,
to which Bohm-Bawerk subscribes, and, in reality, also Jevons
— ^although he appears to be in opposition to it. The latter
view has been zealously advocated by Socialist writers — ^also
by the Americap, F, A. Walker and, ^ven more pointedly, by
his fellow-countryman, Henry George. Among noted European
economists, Charles Gide tends more or less to this point of view.
Those who hold it point to the obvious fact that finished products
are consumed by the workers, and by everybody else, in
proportion to their production, and that there exists beforehand
no fixed and insuperable barrier between those which are
consumed by the labourers (and therefore should, in accordance

^ When, in the third edition of his Positive Theorie de$ Kapitals, p. 632,
Bolm-Bawerk asserts, and even expressly emphasizes the fact that the
capitalist also obtains his income in advance, I cannot understand his reasoning.

If this happened, it would indicate,’ in my opinion, that the capitalists con-
sumed part of their capital — which Bdhm-Bawerk certainly cannot have
meant. His further simile of inducluon currents is much too vague to support
his argument in any way.

PEODUCTION AND DISTEIBUTION 189

with the classical theory, be regarded as capital) and those
which are consumed by the other classes of society.

The foregoing observations concerning this keenly-contested
dispute should show that the truth is not to be found entirely
on either side, though it is nearer to the classical view. In so far
as the product of labour is consumed directly, no capital is
required for the payment of labour — ^and this is largely true
of labour even in the most capitalistic societies, especially of all
personal services and of labour engaged in the final phase of
actual production — e.g. of the baker, and still more of the
shopkeeper who sells his bread. Wages may be said to arise
here by a simple, though indirect, exchange of the commodities
consumed by the worker for the product of his work, which
is more or less simultaneously consumed by the employer or his
customers. Indirectly, it is true, these lalx)urers benefit by the
existence of capital, for when the marginal productivity of labour
is raised, as happens almost invariably with the advent of
capital, this applies, owing to the operation of competition,
to all work performed — even to that for which wages need not
be advanced by capital for any appreciable period of time.
There is, however, no division of the product between labourer
and capitalist — ^i.e. the owner of the circulating capital from
which wages are paid — ^but the labourer enjoys his product
undiminished. Or, if it be preferred, he has to share it only
with the landowner and the owner of fixed capital. (The baking
of bread requires, inter alia, an overL ; the sale of bread,
a specially equipped shop, and so on.) It is, of comrse, not always
so easy to determine the value of a piece of work which is the
last of a long series in production ; we igust have recourse to
the same criterion which has guided us throughout, namely
marginal productivity. By the exercise of greater care in the
baking of bread — for example, by the employment of one more
labourer in the bakery in question — the daily selling value of
the product may, ceteris faribus, be increased by, let us say,
five shillings. After maldng deductions for increased wear and
tear of implements and machinery, cost of increased space, etc.,
this will constitute the marginal productivity of the labour
concerned and will determine, in equilibrium, the wages of this
labour — ^and of aU labour of a similar kind.

In most phases of production, however, there is a longer

190

LECTUEES ON POLITICAL ECONOMY

or shorter interval between the employment of labour and the
final production of an article for sale. Since the labourer does
not usually wait for his wages for the whole of this period,
but more usually obtains them soon after he has performed his
work, it must be evident that he does not obtain them from the
'produd of his labour, either directly or by the exchange of the
product for other products. Strictly speaking, moreover, the
time must be reckoned from the performance of the labour to
the moment when a finished product, ready for consumption,
is brought into being. If, for example, a labourer is employed
in the manufacture of a harvesting machine, the product of his
labour is not really finished when the machine is ready for sale,
but only when the crop harvested with the help of the machine
has been sold and converted into bread. And it should also be
remembered that the same machine will be used for several
harvests and consequently for several years’ baking. Some other
person or persons must thus advance the wages — ^and this, as
the above example shows, for a much longer time than is generally
supposed. It should also be observed that the advancing may,
in the interval, be transferred from one capitalist to another,
as when the harvesting machine leaves the possession of the
manufacturer and passes into the hands of the agricultural
capitalist. That wages (real wages) are paid in products more or
less simultaneously produced si^iifies nothing from an economic
point of view. The modern labourer has, as a rule, nothing to
do with manufacturing these products ; they are the final result
of a series of processes whose various phases of labour have,
as a rule, been paid for. The fruits of these productive processes
belong— with a right which may be disputed by other labourers,
but not specially by the labourer at present engaged — ^to the
capitalist entrepreneur, and may be employed as he chooses,
either for new production — ^in which case he maintains, or even
increases, his capital — or for his own consumption^ If this
consumption, either of his own products or of products obtained
in exchange, is direct, then, of course, the labourers (i.e. those
seeking work in the market this year) will be deprived in
a corresponding degree of an opportunity for consumption.
If it is indirect — ^by exchange for a new, directly consumable
service of labour, e.g. personal services— the labourer will, it is
true, still receive his wages, and it may accordingly appear

PRODUCTION AND DISTRIBUTION 191

indifferent to tdm whether capital is accumulated and maintained
or not — ^provided that there are sufficient products in the market
to pay his wages. But this is a great mistake and to act upon
it would be fatal. For if capital is not maintained by renewal,
then, as it is consumed, the longer processes, which are
characteristic of the present technique of production, must be
curtailed or interrupted one by one ; thus the whole of production,
including the marginal productivity of labour and wages, would
return to the small dimensions of primitive times. Or, more
correctly, the working population — ^which could not possibly
support itself in its present numbers, if we returned to primitive
conditions — ^would, for the greater part, starve to death.

We do not wish to deny that consumers as such can, to some
extent, influence rates of wages by a suitable selection of articles
of consumption. This appears from what has already been said,
as well as from what follows. But their power in this direction
is certainly more strictly limited than is commonly supposed.
Broadly speaking, even if not in detail, we must recognize the
truth of Mill’s well-known principle that demand for commodities
is not the same as demand for labour — ^unless it results in the
accumulation of new capital.

In conclusion, it may be observed that what has been said
concerning the relation of labour to capital applies in exactly
the same way to land. Rent also is advanced by the capitalist
(who may often be the landowner hi mself) in so far as the final
product — ^the product ready for comumjition — ^is brought into
being at a later date than that of the use of the land — as is
usually the case. This is evident from what has been said,
but it is almost always overlooked in economic reasoning —
an error which has contributed in no small degree to a lack
of clearness as to the place of the factors, especially that of
capital, in production.

Such an oversight may easily lead to paradoxical results —
as in the following example, which, for the sake of simplicity,
has been based upon Ricardo’s theory of rent and capital.^

^ The result will, however, be the same if we assume with Bohm-Bawerk
that production takes several years and is continuously progressive. If we
conceive this production as divided into annual parts, stepwise, it will easily
be seen that capital need only amount to a half of the total sum paid out in
wages during the whole penod of production.

192 LECTUEES ON POLITICAL ECONOMY

A capital of 1, 000,000a. gives employment in one-year
production to 1,000 labourers on land for wbicb no rent need yet
be paid. Wages would thus be 1,000a., and if the returns per
labourer are 1,100a. there remains interest for the capitalists
at a rate of 10 per cent per annum. Assume now, however, that
the number of labourers is increased — capital remaining unchanged
— ^to 1,111 men. Wages consequently fall to about 900a. —
whereupon one-tenth of the old capital employed on the land
becomes superduous and must seek investment on new land.
But there only remains (we assume) “ worse land ”, from which
the yield per labourer is only 900a. We should then obtain
the remarkable result that interest, despite reduced wages,
would fall to zerOi not only on the worse land, but all along the
line, in consequence of the competition of capitalists. The whole
of the gain would accrue to the owners of the better land, which
would now receive the diderence in the yield between the better
and the worse land 200a. per labourer, or 200,000a. in all.

If, however, we consider that rent is also advanced from
capital, the result will be quite different. Wages and rent together
will then correspond to the existing capital, or 1,000,000a.,
and since the value of the whole return is 1,100,000 + (111 X 900),
or 1,200,000a., interest will really have risen to nearly 20 per
cent. Rent will continue, in this case also, to be the difference
between the returns from the better and the worse land, but
discounted by one year's interest (i.e. 200 1*2 = 167) for the

area employing one man ; wages, however, will fall to about
750a. Of course, this example is too simple to have any
counterpart in reality and is only intended to emphasise the
principle set forth above.

On the other hand, Bohm-Bawerk is probably mistaken in
the assertion which he makes in the third edition ^ in reply to an
objection of mine, that the advance of rent from capital tends
to raise interest — the sense that interest would be lower if
land were obtained gratis. The exact opposite would happen.
Both rent and wages — or their equivalents in land and labour
— constitute a part of the productive capital on which interest
is paid from the surplus yielded by production. If it were at all
conceivable that all land were free, then all capital would be paid
out in wages and they would thus rise. If in the process there
were no change in the period of production, the surplus product,
and consequently the rate of interest, would be exactly the same
as before. In reality, however, a lengthening of the period of

1 See Positive Theorie des p. 630, note 2.

PRODUCTION AND DISTRIBUTION

193

production would prove economically profitable, and such, a
lengthening would, according to Bohm-Bawerk’s own argument,
lead to a larger surplus product and a higher rate of interest.
If, on the other hand, the landowners did not receive their rent
in advance, but only when production was completed, the rate
of interest would certainly fall, but such a change in the rent
demanded would be equivalent to new capital accumulation
by the landowners, concerning which we refer the reader to
the conclusion of the next section, IV, and especially to
p. 213 et seq,

(4) Our present analysis may also serve to guide us to
a true view of the famous wage-fund theory — once so highly
esteemed, later denied even by its former advocates, then
interred but not yet quite defunct. We have already indicated
that we cannot, strictly speaking, refer to a fund for wages
alone, but only to a wage-and-rent fund. Capital in its free
form is employed to advance both wages and rent ; how much
fails to wages and how much to rent depends upon the
circumstances which determine the present marginal productivities
of labour and land — ^which, in equilibrium, correspond to wages
and rent and therefore absorb without any residue, the capital
which is for the moment /ree — ^i.e. the wage -fund. But does such
a fund really exist ? That it does not exist in reality, as a fixed
and unchanging quantity, follows from the fact that capital
in ail its parts may either increase or decrease, to a larger or
smaller degree, at any given moment. This, however, has not
escaped the defenders of the wage-fund theory. If we imagine
a society under more or less stationary conditions, in which
a given capital in the possession of the propertied classes is
employed year after year without appreciable increase or
decrease, then each year about an equal part of that capital
will be set free. That part (together with the consumable direct
products of labour and land) constitutes the whole production
of finished commodities and services of the year. When the
capitalist class has taken the surplim, corresponding to interest
on its capita], it must, in order to maintain its capital, re-
invest the remainder — ^which it does by hiring labour and
land for new production. This part, therefore, is what might
be called the annual wage-fund (more correctly, wage-and-
rent fund).

194

LECTURES ON POLITICAL ECONOMY

But there cau be no doubt that little is gained in the
explanation of economic phenomena bj the introduction of this
term ; and the simple process by which it was attempted to
determine wages (dividing the wage-fund by the number of
workers) was certainly too elementary. In the first place, as
we have said, the « proportion in which the common fund is
divided into remunerations for the services of labour and land
is by no means given and determined a priori ; and, moreover,
with a change in the amount of capital, the wage-fund may
undergo considerable changes, in so far as the average period of
turrmer of capital is lengthened or shortened. As we have
already shown, there would inevitably be a shortening if by
reason of a diminished supply of labour (due perhaps to
emigration on a large scale) wages rose, other things remaining
the same. In other words, a reduction in the divisor would
itself bring about a reduction in the dividend, though not quite
in the same proportion. But, on the other hand, a reduction
in the number of labourers would increase the distributive
share of labour, not only at the expense of the capitalists, but
also — ^perhaps to a greater extent — at the expense of the
landowners. Hence the advice which the advocates of the
wage-fund theory gave to the labourers, namely to limit the
supply of laboox in the market in their own interests, was in
itself, good advice, even though based upon inadequate
reasoning.

It would also be possible to regard all capital, as Bohm-
Bawerk does, as wage-fund. But this amounts to the same
thing ; for in any case it is only the part annually set free which
can purchase labour (or land).

The real error in the classical wage-fund theory was, as
Bohm-Bawerk pointed out, that it frequently identified the
wage-fund with capital as a whole, although it conceived the
wage-fund to be invested for only one year. A very striking
example of this is Senior’s “ last hour ”, immortalized by Karl
Marx.^ Senior thought he could prove that a shortening of
working hours per day by about one-eleventh would reduce the
profits of capital from 10 per cent to nothing. He based this
conclusion on the absurd assumption that all capital, including
that invested in factories and machmery, has a one-year turnover,

^ Das Kapitaly i. Third edition, p. 206 et seq.

195

PEODUCTION AM) DISTEIBUTION

wMcli did not prevent Mm from calciilating, in addition^ annual
depreciation for wear and tear on buildings and macKinery.
If we caicnlate correctly, with tbe figures advanced by Senior,
we shall obtain for fixed capital a period of turnover of about
8 years (sixteen depreciation allowances) and, for capital as a
whole, 7 years. Ceteris panbus, a reduction in^the hours of labour
would certainly reduce the profits of capital, but only from 10 to
about 8 per cent, and with somewhat greater intensity of work
not even by so much as this.

It is curious that Marx Mmself does not seem to have observed
the yawning gap in Senior’s argument, to which he devotes
a prolix refutation. Or perhaps he hesitated to point out an
omission the revelation of which would inevitably have exposed
the weakness of his own “ exploitation theory

Another criticism which has been made against the wage-fund
theory is that it is correct only on the assumption that the
labourers take their wages in kind at the same time as they render
their services. If, on the other hand, they wish to take their
wages partly or wholly in capital ” — ^in other words, to wait
for their wages until their own product is ready for market —
then wages may, within the limits of what is produced, rise to
any height whatever and be independent of the size of the
wage-fund or capital. This is of course quite correct, but it is
scarcely a proper objection to the wage-fund theory, except in
its most rigid form ; for, by such a procedure, the workers would
themselves become capitalists and would build up capital, so
that the fruits of their labour wMch were not exchanged for
products, i.e. for a part of the existing capital, would constitute
a real addition to it.

This method of paying wages is the essence of the profit-
sharing system, and if it has occasionally had beneficial results
this may perhaps be most simply explained by the fact that the
system stimulates the workers to accumulate capital, whose future
fruits are usually sweet, even if its roots in the present are
bitter.

Later on, we shall discuss the accumulation of capital —
wMch is an important element in the theory of capital. But we
will first return to the theory of exchange and see how tMs
appears when it is linked up as it ought to be with the theory
of production outlined above.

196

LECTURES ON POLITICAL ECONOMY

3. The InterdependeTice of Prcduction and Eo^chaTige, The Theory
of Exchange Value in its Final Form

Hitlierto we Lave been reasoning on the assumption that
production is carried on at given prices for all products. We must
now drop tMs assumption and approach the real world — ^in which
production and exchange mutually affect each other. Whilst
we thus obtain a more complete theory of distribution, modified
in some respects from that set out above, we shall also have an
opportxmity of resuming and completing our discussion of the
theory of exchange value, which we were compelled to interrupt
at the point at which its dependence upon, and connection with,
the theory of production and distribution became clear. We
shall, however, restrict our observations to the problem of the
production and exchange of only two articles ; the argument
is much facilitated by such a simplification and there is no
theoretical difficulty m subsequently extending it to all the
infinitely varied products which are actually exchanged. In spite
of this simplification, however, the problem resolves itself into
two essentially different questions, which are best surveyed and
treated separately. On the one hand, we may assume that the
two articles exchanged are produced in different coimtries or
districts, between which there is no transfer of labour or capital,
so that all the resources available in each community are engaged
in the production of one article. On the other hand, we may
aasume that the production of both articles takes place in a closed
economy in such a way that land, labour, and capital can be
transferred from one industry to the other. The former case is
typical of what is usually called in economics the theory of
international trade and international values ; the latter of the
theory of internal exchange under free competition, ’it is
unnecessary to add that neither of these abstract assumptions
corresponds to the phenomena of the real world. Perfect
mobility of labour and capital within one coimtry is just as
improbable as is the complete absence of such mobility between
countries.

Let us first assume that each coimtry, owing to natural
conditions, is compelled to produce one commodity only. It is
then clear that under free competition every producer will
endeavour with the available means to obtain the maximum

PRODUCTION AND DISTRIBUTION 197

net profit, whicLi, in eqniHbriiim, must cause tlie whole production
of the country to reach its maximum. It is true that we have
only proved this on the assumption of production without
capital, but it will easily be seen that its essence remains
unchanged, like the objection of Ricardo, which it was our purpose
to refute, even if the argument is apphed to capitaKstio
production.^ What has been said will by no means apply if
production and exchange are effected co-operatively, or if the
producers are otherwise associated in trusts or cartels ; the
country would then have to be regarded more or less as
a monopolist with respect to the commodity in the production
of which it has greater natural advantages than other countries.
Production would therefore be carried on with reference to the
most advantageous monopoly price ; a contraction of production
might be to the advantage of the country even if all the available
factors of production were not employed. If each of the two
countries monopolizes the production of one commodity,
then pricing is theoretically indeterminate ; we have in fact
reverted to isolated exchange, with the further complication
that not even the quantities available are given beforehand,
since they are the objects of production. If there is free
competition, then, in accordance with the law of production
and exchange, each country will produce as much as possible
of its own commodity and exchange will be effected at the price
which will normally equate supply and demand. It might well
be that a restriction of the production of one commodity would,
if simuUaneomly undertaken by all, be to the advantage of all
producers of this commodity ^ ; but restriction by an individual
producer must, ceteris faribus, do him harm, since his supply
does not appreciably affect prices. This would also be the case
if the country manufactured several commodities, whose relative
exchange values must be taken as given for the individual
producers.

We have, therefore, simply to combine the foregoing laws
of production for a single commodity (or for several commodities
whose relative prices are given) and the laws of market value
of a given stock of goods. The former determines the quantity
of goods which accrues to each individual in each country in the

^ [A mark against this passage in the author^s copy of the second edition
indicates that he wished to reca^ it.]

* Honrs of labour may be influenced by the possibility of exchange.

198 LECTURES ON POLITICAL ECONOMY

form of wages, rent, or interest ; the latter then determines
the quantities of goods which will be mutually exchanged, and
the relation between them — ^which constitutes international
exchange value. The theory of international trade — or, more
correctly, the abstraction so called — ^is therefore much simpler
in principle than the problem of exchange in the internal market,
in which the free transfer of the factors of production from
one commodity to another must be presupposed. That the
earlier economists thought otherwise was due to their erroneous
idea that cosls of production, which were assumed to regulate
exchange value in the home market, could be determined on
grounds independent of exchange value itself.

If I, r, and i represent the rate of wages, rent, and interest
in one country, and A, B, and 0 the available quantities of
labour, land, and capital, then A A, B.r, and C.i are the total
quantities of wages, rent, and interest in the country, expressed
(like capital itself) in terms of the one commodity produced in the
country (or in one of them if there are several). Personal
distribution will depend on the labour performed, or upon the
land or capital owned by each individual. In the other country,
the annual supply of the product of each person will be determined
in the same way, and since the personal dispositions of all the
individuals as regards consumption must be taken as given, we
thus possess all the necessary determining factors for establishing
the price and the quantities exchanged.

A close comparison between the above theory and Mill’s
treatment of the theory of international trade ^ is of great interest
and afords, at the same time, a striking proof of the need for
a more carefully-developed theory. In the first two editions of
the Pfinctples, as in an earlier treatise on the same subject, Mill
set up a theory which, so far as it goes, fully accords with the
assumptions made above. The various factors of production
cannot, on these assumptions, pass from one process of produc-
tion to another ; and consequently, says Mill, the necessary
pre 2 ?equisite for determining the relative prices of goods by their
relative costs of production is absent and we must fall back on
the more general law of supply and demand. If there is
equilibrium between supply and demand under such conditions
that the supply of each commodity always increases when its
price rises (and vi-ce versa) then equilibrium will be stable. A relative
increase in the price of one commodity would lead to an increased
^ J. S. Mill, Principles, book iii, chap* xviii.

PEODUCTION AND DISTRIBUTION 199

supply but, on tbe other hand, to a decreased demand ^ for it ;
a lower price would similarly lead to diminished supply and
increased demand, so that, in both cases, prices would tend to
revert to the original level. So far so good. But in this connection.
Mill considered the case m which an increase in the relative price
of one commodity {A), and consequently a decrease in the relative
price of the other commodity (B), does indeed lead holders of
(A) to increase their demand for (B), but at the same time it
causes them to decrease their offers of (A) because their need
for (R) now rapidly approaches satiation ; thus equilibrium
between marginal utilities is achieved before the offers of (A)
have reached the same level as before. One of his critics,
W. Thornton (who by his later criticism induced Mill to abandon,
somewhat too hastily, his wage-fund theory), pointed out that,
under such circumstances, equilibrium between supply and
demand would, even when other things were equal, be possible
at more than one price. If, at first, 17 units of (R) exchange for
10 units of (A), but the price of (R) happens to fall, so that 18 units
of (R) must be given in exchange for 10 units of (A), then, on
Mill’s assumption, it might happen that holders of (A) would
reduce their offers of (A), though at the same time holders of
(R) would certainly diminish their demand for (A) ; and it is
quite conceivable that equilibrium between demand for and supply
of (A ) — and eo ipso of (R) — would also occur at this new price.
To us there is nothing remarkable in this. The case considered
by Mill is, in fact, exactly the same as the one we have considered
above, in which the supply and demand curves intersect when
the former begins to fall ; and we know that when this happens
it is quite possible that the curves will intersect at more than one
point. Mill, however, without further examination, derived from
Thornton’s remark the unfortunate conclusion that equilibrium
between supply and demand would occur under such circumstances
at any price — ^which can only be so in quite exceptional cases.
In other words, he assumed that the problem is essentially
indeterminate, so that more than the above dcUa would be required
to determine international exchange values.

He therefore undertook to complete his theory in this
direction, but without success. It has justly been remarked
that the latter part of Mill’s chapter “ On International Values ”,
which he added to the third and subsequent editions of his
Principles, really contains only a repetition, in a new form, of

^ Strictly speaking, this applies only if the two commodities cannot
substitute each other in consumption.

200 LECTURES OX POLITICAL ECOXOIIY

Tirhat lie had alreadj said elsewhere. Besides reciprocal demand,
there :s, :n his opinion, another relevant factor — the means of
satisfying ihzs dewjivd, set free in each country by the re-onentation
of its .ndnstry. Y?liat he really adds, however, is only a particular
arbitrary assumption as to the relation between the price of
a cominodity and its supply and demand. He assumes that the
supply of each commodity is entirely independent of its price
and that demand is in inverse proportion to the price of the
commodity ; as though each economy first satisfied its need for
the commodity which it manufactured itself and then disposed
of the surplus at any pHce

Graphically represented, this would mean that the supply
curve of each commodity would he a line parallel to the price
asis and the demand curve a rectangular hyperbola. On this
assumption, it is clear that the two curves can only intersect
at one point and that the price equilibrium is stable. But in
that case we should find no expression for the fact that a rising
price of either commodity might lead its owners to reduce, instead
of increasing, their supply. In reality. Mill neglects the whole
of this question, which was, after all, the very startmg-point
of his investigation, and begins instead to inquire which of the
two countries would profit most by a change in price caused by
different conditions of production for one of the commodities.
But in this way he finds no use for the new determining factor
which he wishes to introduce, and he is finally forced to the
almost pathetic confession that “the new element, which for
the sake of scientific correctness we have introduced into the
theory of international values, does not seem to make any very
material difference in the practical result But, as we have
said, he has not really introduced any new element at, all ; not
only the practical results of his inquiry, but the theoretical
results too, are entirely unchanged.

On our assumptions of free competition and immobility of
the factors of production there are, indeed, no determinants of
price except equilibrium between supply and demand. This is
su:Scient for a theoretical solution of the problem, although the
possibility of several solutions, usually only a finite number, is not
excluded.

Somewhat more complicated, at least at fiorat sight, is the
other problem, of ascertaining the relation between production
and exchange in the “ home market i.e. on the assumption
that the available factors may be freely transferred from the
production of one commodity to that of the other. And yet

PEODUCTION AM) DISTEIBUTION 201

the main lines of the solution are simple enough even herCj
although — ^as the history of the science shows — ^they are nor
so easy to discover. If we suppose, for a moment, that a given
proportion of the available labour, land, and capital — ^i.e., in
the last resort, given quantities of original factors of different
years — ^is always used in the production of the one commodity
and the remainder in the production of the other commodity,
then the problem of equilibrium price and the quantities
exchanged would be exactly the same as in the preceding case.
In other words, for every such hypothetical distribution of
factors of production we should have one or more possible
solutions. Now, in this case, the distribution of the factors is
precisely one of the quantities required for the solution of the
problem, though we find instead three new conditions, or logical
relations, which must be satisfied : namely, the requirement
that rent and interest shall be the same in both branches of
production, which cannot be assumed where two countries are
concerned.^ Every conceivable distribution of the factors
gives rise, in each branch of production, to certain rates of
interest, wages, and rent — expressed, in the first instance, in
terms of one of the goods produced but also expressible in terms
of the other since there is an exchange relation between the
commodities, which follows from the same assumption ; it is
clear, therefore, that the problem is completely determi n ate
by the equation of these three quantities individually. It should
be capable of mathematical solution as soon as all the other data
(the total productivity of land, labour, and capital, their
distribution among individuals, and personal preferences in
consumption) are exactly known. In reality, this problem of
equilibrium may also be solved by trial and error ; so long as
wages, rent, and interest are greater in one branch of production
than in the other, labour, land, and capital will flow into the
channel where they reap the higher reward and there will be
a simultaneous adjustment of relative exchange values, so that
equilibrium will finally be achieved as far as is generally possible.

In order to avoid any misconception, one more observation
should be made. The fact that the form of capital may change,

^ In the article “ Handel ”, in Schonberg^s Handbuch (cf. Ehowymiaha
SamhdUslivet, ii, p. 478), W. Lexis has been gtdlty of a serious omission in
relation to tMs point, winch makes his argument deceptive.

202 LECTURES OX POLITICAL ECONOMY

that labour-capital (i.e. saved-up labour) may be, to a certain
extent, replaced by land-capital (i.e. saved-up natural resources)
and, vice versa, that capital investments (or capital-goods) of
shorter duration mav be exchanged for those of longer duration
— ^these do not introduce any element of indeterminateness
into the problem ; for, in each particular branch of production,
they are all governed by the general economic principle which
we have already developed in the treatment of production.
It may well be questioned what importance we are to attach
to the ciaim that, under stationary conditions, the amount of
capital must remain constant from year to year. But here we
must distinguish two different tilings. In equilibrium, the capital
employed in production has already assumed a certain technical
dimension and composition, as well as a certain exchange value
(expressed in terms of one of the commodities). It can now be
asserted that, so long as capital of this magnitude and
composition, or even of this exchange value, is mamtained and
utilized from year to year, equilibrium cannot be disturbed if,
from the beginning, the other conditions of stability are fulfilled.
But it would clearly be meaningless — if not altogether
inconceivable — ^to maintain that the amount of capital is already
fixed before equilibrium between production and consumption
has been achieved. Whether expressed in terms of one or the
other, a change in the relative exchange value of two commodities
would give rise to a change in the value of capital, unless its
component parts simultaneously underwent a more or less
considerable change. But even if we conceive capital genetically,
as being a certain quantity of labour and land accumulated in
different years, a change in the value of commodities would also
alter the conditions of their production and thus necessitate
a larger or smaller change in the composition of capital.

This indeterminateness — which was inherent in our first
main example,^ and even in the pure problem of production —
is, of course, primarily due to the fact that capital, unlike labour
and land, is not an original factor of production which can
exist (even hypothetically) independently of, or antecedently to,
production. Its origin and maintenance inevitably presuppose
that production is taking place. But it also has another, more
deep-seated, cause. In reality, the amount of capital is not
^ That of International Trade.

PRODUCTION AND DISTRIBUTION 203

determined by physical conditions, but by the equilibrium
between psychical forces which, on the one hand, drive ns to
save and accmnnlate capital and, on the other, to consume
already existing capital. In other words, the accumulation of
capital is itself, even under stationary conditions, a necessary
element in the problem of production and exchange. We have
now reached a point in our exposition at which this new factor
forces itself upon our attention. We shall, therefore, consider
this subject in our next chapter — ^though the laws of capital
formation have been too little studied for a treatment of the
subject in its entirety to be of much real use.

We consider the total amount of a commodity produced
as a function (homogeneous and linear) of all the quantities
of labour and land employed (i.e. annually consumed) both current
and saved up. We then obtain for one commodity

jP = <I>{Aq, Ai, A^ • • * Bq, B^ . . . )

in which Aq and Bq indicate current services of labour and land,
A I and Bj services one year old, etc. The partial derivatives
of this function with respect to each of the quantities included
gives us the wage (Q, and ‘the rent per unit of land (r), payable in
this industry, expressed in units of the product, and also the
marginal productivities of all the constituents of capital. From
these we can deduce the rate of interest which is payable (i).
With the relation which must exist in equilibrium between the
yields of capital-goods of different duration and between the
yield of land-capital and of labour-capital, we are now in a position
to express all the above quantities m terms of three of them
(e.g. Aq, Bi, and A^). In the same way, we obtain for the other
commodity : —

P^^^A\,A\,A\ . . . B\,B\,B\ . . . ),

from which we can determine the values of F, and for this
industry, and being expressed in units of the second
commodity ; and can similarly express all the quantities included
in terms of three only — A^q, B\, A\.

The number of unknowns is thus reduced to six only. To
determine them we have the following additional relations.
In the first place, under stationary conditions, the sum total of
the quantities of labour annually consumed — current or saved up
— ^must be equal to the supply of labour annually available in the
coimtry ; and the same applies to the land which is employed

204

LSCTUSES OX POLITICAL ECONOMY

eithei in iis original or capitalized form. If the country has at
Its disposal A units of labour and B acres of land, we therefore
obtain : —

Ao - A, 4- A2 -r . . -4 A\ -f Ai\ “r • - • = A

and

= B.

By iTLttTis of the other data we can also express the exchange
Talue of the two commodities as a function of the above quantities
and therefore dually in terms of our six unknowns. If we represent
this exchange value (e g. the price of the latter commodity,
expressed :n terms of the former) by p, and if wages and rent
are identical in both industries, then : —

I = p and T = p.rh

The rate of interest must also be the same in both ; thus i ==

We have thus obtained five independent relations, but we
still require a sixth. This can be obtained from our assumption
concerning the amount of capital. The quantities A^, Aq . . .
Bj, B2 . . ., etc., are only those parts of capital which are annually
consumed. Corresponding to them, under stationary conditions,
there must exist other parts of the total social capital, whose
amounts can be exactly determined. There must be one more
element corresponding to A 2, ttvo more elements corresponding
to A3, three to A4, etc., and similarly as regards Bg, B^, etc.
(cf. Fig. 12). In equilibrium, the composition of the sum total
of capital is thus definitely fixed. AH its parts can be expressed
separately either in the fimt three or m the last three of our six
unknowns. If, for example, we now wish to impose the condition
that m equilibrium the sum total of capital shall have a certain
exchange valiie, measured m terms of one of the products, we need
only calculate the exchange values of all parts and add them.
These exchange values are (in accordance with the above) the
original exchange values of the portions of capital concerned,
plus accumulated interest. Thus, for example, the present portion
of capital indicated by A3 has the exchange value A3.Z.(i + if,
ihe two identical portions also represented quantitatively by
A3, since they represent equal quantities of saved-up labour,
have, on the other hand, the values A3,l.(l+^f and
A3.L{l+^), respectively. The portion of capital repre-
sented by B3 has the exchange value jB3.Z^.n.(l + =
B^.l,(l -j~ iff etc.

If these values are summed and are put equal to a certain
given quantity — ^the total exchange value of the capital employed

PEODUGTION AM) DISTRIBUTION 205

in the two industries together^ expressed in terms of tlie first
commodity, we shall then obtain the necessary sixth relation,
and the problem will at last be completely determinate.

If it were permissible to calculate with simple interest, the
problem would be simplified in so far as the accumulation of
capital through time need not be taken into consideration —
though its distribution as labour-capital and land-capital, advanced
wages and advanced rent, must ; we should then only have to
deal with the average period of investment.

It may perhaps be asked whether, in a case such as this
(in which both commodities are manufactured in the same
country), more than one relative equilibrium price is possible.
This is quite conceivable if — as is usually the case — wages,
rent, and interest enter into the manufacture of the two
commodities in different proportions. If the prevailing equilibrium
persists, and a higher relative price is paid for one commodity,
then, obviously, that factor (or factors) which enters into the
production of the commodity in relatively large amounts is
favoured at the expense of the others.

As will easily be seen, there is no difficulty in extending
the above reasoning to any number of commodities. Under the
designation of commodity we may also include the factors of
production themselves when they are directly employed by their
owners. We can therefore abandon the simplifying assumption
hitherto made — viz. that all factors of production on the market
are available in given determinate quantities, which are offered
in their totality by their owners, irrespective of the price they
will fetch. This is very important, especially for labour, for we
can now consider the case m which the hours of labour are
variable and determined by the workers themselves, on the
basis of the equality of the indirect marginal utility of work
and the direct marginal utility of leisure.

Just as exchange and exchange value thus assume their
final form by their connection with production, so, of course,
exchange for its part considerably modifies the production and
distribution of the product. Each producer — ^labourer, landlord,
and capitalist — ^receives a substantial increase in utility from
the possibility of exchanging the commodities, in the production
of which he participates, for others (production in the modem
sense would indeed be inconceivable without this possibility,

206 LECTUKES ON POLITICAL ECONOMY

for nowadays production is carried on almost solely for exchange).
And further, the relative distribution of the product between
the three classes of producers becomes quite different, when
there is a possibility of exchange with other districts or countries.
A well-known example of this is the fall in rents, to the
advantage of the landless classes, which has occurred in parts
of Europe, as a result of the importation of foodstuffs from extra-
European countries. Another is the more doubtful, but perhaps
equally real, case in which the workers, or the great masses of
the population in the latter countries, have suffered from the
supply of cheap manufactured goods from Europe, to the
advantage of the landowners.^

^ See my Finanziheoreiische. UnterawchungeTif pp. 63 ff. (Jena, 1896).

PART III

ON THE ACCUMULATION OF CAPITAL

Bibliography. — The literature on this subject is very meagre.
Among earlier writers there is virtually only H von Mangoldt
(Volhswirtschcifislelire), and among recent writers, Bohm-Bawerk
{Positive Theorie des Kapitals)^ who have devoted detailed
attention to the accumidation of capital, Karl Marx, Das
Kapital, voL i, section 7, Der Akkumulationsprocess des Kapitalsj
also deserves attention, despite his bias and exaggeration.
Compare also Wagner, Grundlegung, part ii, vol. hi. In
Schonberg’s Handbtcch the whole theory of the accumulation
of capital is despatched in a single page, and in Conrad s
Handworterbiich der Stcmtsmssenschaften in a single column.
Gassers The Nature and Necessity of Interest contains a note-
worthy attempt to carry discussion on some points further
than had previously been done. The best material for an
examination of the problem is probably to be found in the
statistics of banks, and especially savings banks, as well
as in statistics of capital wealth, though the latter are
unfortunately extremely sparse and rudimentary.

So far, our discussion has been based on the assumption
that productive capital, like the two other factors, is constant.

. In reality, however, capital is not, like land — ^and, for shorter
periods, labour — ^physically limited. It can be increased at any
moment by saving ; it can be reduced by unproductive
consumption. Neither is the supply of capital renewed in the
same way as the supply of labour, by the work of nature —
although it is natural to accumulate capital at certain periods
of life (particularly middle age) and to consume it at others
(early youth and old age). A rational theory of saving is thus
necessary before we can clearly understand the conditions of
a stationary society, with a constant supply of capital ; and still
more, of course, before we can understand and foresee the gradual
changes in the amount of social capital.

Unfortunately, such a theory has not been worked out, and
tl^,; phenomena which it should explain depend on a number

207

208 LSCTUEES ON POLITICAL ECONOMY

of motiTes — partlj selfisi, partly altruistic, but in any case very
complex. People save for themselves, but also for their successors.
Some 060010 often save merely for the pleasure of saving.
Exceptional people may save and accumulate capital simply
because they cannot help themselves — e.g. certain multi-
millionaires whose capacity for consumption even the ingenuity
of the luxiury industries cannot stimulate. Large families
encourage thrift, because a source of income, say a landed estate,
which has hitherto supported the family, may now be inadequate
for that purpose. But, at the same time, a large family frequently
constitutes an insuperable obstacle to saving, since every available
source of income is urgently and immediately needed. On the
other hand, If the capital in an indivuduars possession is already
so great that only a small portion of its yield is required for the
maintenance and expenses of the family, then it will grow of
itself — at least at present rates of interest — at such a pace that
even great fecundity in the family cannot keep pace with it.
The ever-growing wealth of certain multi-millionaires is therefore,
from a social point of view, a not inconsiderable danger to society.

Among the many influences affecting the accumulation of
capital, the rate of interest is undoubtedly one — although even
its influence is uncertain and ambiguous. Theoretically, the
individual should always carry his accumulation of capital (or it
may be his consumption of capital) to the point at which the
present and future marginal utflities of the goods saved is equal.
By sacrificing one shilling this year he can, for example, count
upon obtaining two shillings in ten or fifteen years. The question
then becomes whether, at that Ume, two shillings will have more
or less subjective value for him than one shilling now. The
answer to this question naturally depends on a number of
circumstances over which he himseK can exercise some influence
— such as the savings which he is likely to make during the
immediate feriod. Here the rate of interest has a two-fold
influence ; a high rate increases the yield of present saving and
consequently its future marginal utility, i.e. the future utility
of the last unit of capital now saved ^ ; but, on the other hand,

^ Cassel IS not quite correct when he says : “ A man who attaches the
same importance to future needs as to present ones, if he expects to be able
to provide lor his needs in the future just as easily as he does now, has no
reason for setting aside anything of his present income ” (op cit., p. 141).
This argument actually presupposes the absence of any rate of interest.

CAPITAL ACCUMULATION 209

at a given rate of saving, it makes provision for the future
more ample and thus reduces the marginal utility of future goods
for that individual. The latter tendency may even outweigh
the former, so that, for certain individuals, a low rather than
a high rate of interest may act as a spur to the accumulation
of savings.

Individual saving is therefore a very complicated
phenomenon. But if we consider society as a whole, and regard
its average economic conditions as approodmately stationary,
the progressive accumulation of capital must be regarded as
economical so long as any rate of interest, however low, exists.
For the average individual, or rather for society as a whole
(regarded as an individual who never dies), the accumtilation
of capital presupposes the exchange of a lower marginal utility
for a higher — ^provided that it is not too rapid and does not
absorb too much of the present means of consumption. Under
such conditions, we should therefore expect a continual
accumulation of capital — ^though at a diTniniRbing rate — and,
at the same time, a continual fall in the rate of interest.

In The Nature arid Necessity of Interest^ Cassel adduces
certain apparently very striking reasons why a heevy fall of
interest rates is not to be expected in the future. He rightly
points out, in the first place, that every fall in the rate of interest
causes a number of long-term investments which were previously
unremunerative to become profitable ; and every such large-scale
absorption of free capital naturally acts as a brake on a further
fall in interest rates. He especially observes that a general
demand for larger houses^ entailing extensive building operations,
would arise if, as a result of a heavy fall in interest rates,
expenditure on houses is practically restricted to the mere costs
of maintenance — ^and site rent. To this it may be objected that
larger premises, at least in our climate, involve various other
outlays, especially for fuel and light, which are often as
considerable as the rent itself. Increased housing accommoda-
tion for the poorer classes, however desirable it may be in itself,
is therefore scarcely to be expected, unless their level of income
can be raised. With certain reservations, however, this part of
CasseFs reasoning is undoubtedly correct — ^though it evidently
sets no limit to the downward trend of the rate of interest, but
only relates to the rather slow tempo at which the movement
may be expected to occur.

210 LECTUEES ON POLITICAL ECONOMY

The latter part of CasseTs argument would be of much
greater importance here — ^if it could be regarded as correct.
He considers (in agreement with the classical economists) that,
with a certain rate of interest which is not too low, the very
desire or ability to accumulate capital practically disappears, so
that the rate of interest could not fail lower.

The case which Cassel exclusively considers is that of a business
man who in his prime has accumulated a fortune, upon the yield
of which he lives after he has retired from business. If the rate
of interest is sufficiently high, he can do this without in any way
encroaching on his capital. He may therefore have the satisfaction,
or indulge in the vanity, of leaving it undiminished, or perhaps
even augmented, to his heirs : the interest alone is quite sufficient
for his needs. If, on the other hand, the rate of interest should
materially fall, say to 2 per cent or per cent, then, says Cassel,
such conduct would usually become impossible. Either the capital
must be so great that the efforts or good fortime of a single
individual would seldom suffice for its accumulation ; or else
the mere yield in interest will be so small that he could no longer
live on it without a serious change in his habits of life. He will
therefore live on his capital, e.g. by the purchase of an annuity —
Cassel shows, by detailed figures, how strong the temptation
would be, since at so low a rate of interest he could multiply
his annual income. And, says Cassel, he has a perfect moral right
to do so. As a rule, he has already provided for the education
of his children and perhaps for establishing them in life. He
does not owe them more than that. On the contrary he may
justly expect that they, in their turn, will act in the same way
as he : work and accumulate a fortune during their youth and
middle age, and consume it in their old age after they have
provided for thdr children’s education.

CasseTs argument may roughly be presented in this form.
That it is correct in some cases cannot be denied, but as a general
argument it can scarcely be accepted, for it is evidently based
on the assumption that most fortunes are the fruit of the work
of a single generation. But this is not the case even nowadays,
and it evidently becomes less and less conceivable in proportion
as the rate of interest falls. If we assume that the capitalist
has inherited the whole or the greater part of his capital, the
conclusion will be quite different. By consuming it, or even by
failing to increase it, he would usually put his children in a more
■unfavourable position than he had himself occupied. This, however,
conflicts with such an elementary impulse in human nature that

CAPITAL ACCUMULATION 211

we can safely assume tliat it will not nstialiy occur. It is, therefore,
rather difficult to imagine, even in a society based on private
property, any hmit below which the rate of interest could not fall,
because the accumulation of capital would come to an end. We
shall endeavour to show that the degree or rapidity of its fall
depends mainly on an entirely different circumstance, which is
scarcely mentioned by Cassel ; namely the degree of probability
with which we may expect the future growth of population to be
on the same or a similar scale to the present.

If, however, the facts are not quite in accordance with
theoretical speculations (such as those on p. 208) and if, in
particular, the long-prophesied ideal of economists, in which
interest will have fallen to a minimum, is tardy in its realiza-
tion, the cause is presumably to be found in the following
circumstances. In the first place, there is the effect of the
subjective uvdervahmtion of future needs and overvaluation
of future resources, which was observed by Bohm-Bawerk,
This, in turn, is primarily due to the fact that, to the individual,
the future is always in a high degree uncertain. He does not
know whether he himself, or those in whose weU being he is
most interested, will really profit by his sacrifices. Moreover,
even if capital accumulation as a whole increases production,
the return on individual capital accumulation, even the technical
return, is uncertain. The enterprises in which capital is invested
may perhaps yield large profits if they are very successful ; but
the chances of such success are not very great. And since, in
accordance with the general law of marginal utility, the
possibility of a loss of wealth outweighs, for the individual,
the prospect of an equal gain, such an enterprise, from the
point of view of individual business, must always be regarded
as unprofitable unless the chances of gain considerably exceed
those of loss. This is probably the general rule. The special
inducement which hazardous enterprises offer to gambling or
adventurous spirits is a compensation, but operates perhaps
more in the destruction than in the accumulation of capital. In
this connection, we need only call attention to the large extent
to which the modern concentration of capital and the credit
and insurance system stimulate and facilitate saving by let'elling
out and reducing these risks to a minimum.

In these respects, however, a collectivist society would

212 LECTURES ON POLITICAL ECONOMY

afford a mncli better guarantee for tbe rapid accumulation of
capital tban does the existing individualistic society. The capital
saved by united efforts would equally benefit all individuals
and the whole of society in the future ; and the failure of some
enterprises would be of little importance, if those which succeeded
yielded a correspondingly greater return. Though this is opposed
to current opinion, it is precisely in a collectivist society that we
should expect a progressive accumulation of capital until
production was fully supplied with new capital and the national
dividend reached its technical maximum — assuming that interest
in the well-being of future generations was not less than in
existing society.

Another reason why interest is still comparatively high is
the fact that states destroy capital (especially in war and
armaments) at the same time as it is being privately accumulated.
The enormous national debts contracted by European and
extra-European states in the course of years (especially for
purposes of war) naturally presuppose a more or less corresponding
amount of savings on the part of subscribers (though it is true
that war-loan is generally issued below par) ; but they do not
represent any really productive capital, only a claim by certain
citizens on present and future generations of taxpayers. In this
connection it may be asked, at least when the rate of interest
begins to decline more rapidly than capital increases, and the
earnings of capitalists consequently decline absolutely, whether
this must not act as a brake on further capital accumulation.
In purely abstract theory this would not be the case in an
individualistic society in which each individual manages and
saves on his own account. If a particular individual increases
his capital, the effect on the rate of interest is not appreciable.
The result of his saving will therefore be an unconditional
gain for him. On the other hand, it cannot be denied that
capitalists as a class will gladly welcome all measures destructive
of capital, such as armaments and war — ^for which they will
largely be compensated by the State's contractual obligations,
and which will help to raise the rate of interest. This constitutes
a not inconsiderable political danger, as Adolf Wagner pointed
out. But the collectivist state will be qmte unaffected by
a lowering of the rate of interest as such, smce all sources of
income would be more or less common to the whole community.

CAPITAL ACCUMULATION 213

and, in such a case, the other sources would necessarily increase
in a more than corresponding degree.

But the most important reason why the rate of interest has
not fallen is probably that our modem societies difEer in a high
degree from the stationary type. Hitherto, we have only
considered capital accumulation on the assumption of completely
stationary conditions ; if we abandon this assumption the
problem becomes essentially different. For example, if a country
for some reason, such as the successive exhaustion of the land,
passes from a JiigheT to a lower degree of productivity and
prosperity, then the same quantity of commodities will have,
on the average, a higher marginal utility, and consequently
a higher subjective value, in the future than in the present.
The mere retention of consumption goods for future use thus
becomes advantageous, although it cannot, of course, give rise
to increased productivity and therefore cannot, in the usual sense,
yield any interest. Even in our day, people always save stocks
for the lean season, and it was formerly very common to save
grain for bad years — a custom which in countries with bad
communications, such as India and Russia, may still be necessary.
If, on the other hand, a country passes from a lower to a higTier
degree of prosperity independently of the growth of capital (as
a result of technical discoveries, etc., or when a colony is first
peopled) capital accumulation may be uneconomical, even though
technically it might give rise to an increased productivity of
labour and land. A larger quantity of products might then
represent a lower marginal utility, since prosperity as a whole
had increased.

Again, if the growth of population is accompanied by an
increased demand for all kinds of products, on the one hand,
and by an increased supply of labour available in the future,
on the other, then a capital accumulation which might have
brought down the rate of interest to practically nothing under
stationary conditions will not now be sufficient to do so ; or
will only just suffice to maintain capital at about the same
relative level, for which reason it will continue to possess a high
marginal productivity and to yield a high rate of interest. In
addition, capital accumulation is here impeded by the number
of unproductive consumers, large ffimilies, etc. If both these
causes operate (increased productivity and great increase of

214 LECTUEES ON POLITICAL ECONOMY

population) as oft-en happens in flonrisliing colonial lands, since,
np to a certain point, the increase of population in itself brings
improved technical conditions of production, the rate of interest
may be incredibly high for a long period — as high as 50 per cent
or more — ^as Adam Smith observed in the North American colonies.
The marginal productivity of capital here is extremely high, yet
capital is not rapidly accumulated, but remains just as inadequate
in relation to demand. Everybody rightly expects that his own,
or his children's, economic condition will automatically improve
in the future, and nobody therefore considers it desirable to
sacrifice the moderate provision which he is able to make at
present for himself and for them. Capital loans and investments
from older countries with a lower rate of interest soon flow in,
moreover, and counteract, in a greater or lesser degree, the
conditions which we have just described.

But it is clear that these cases are ail only exceptions to the
rule. The unprecedented growth of population recently witnessed
in Europe, and still more in certain extra-European countries,
will certainly, sooner or later — ^probably in the course of the
present century — prepare the way for much slower progress and
possibly for completely stationary conditions. Then interest will
also fall, and the capitalist will have to be content with quite
a small share in the product — ^both absolutely and relatively —
and perhaps (though, for the reasons given, this is somewhat
improbable) with nothing at all. But this, of course, would not
render capital unnecessary for production. On the contrary,
it would then have attained its maximum importance ; for just
as land, when it is in excess, yields its products gratis or for
a very low compensation, so a perfected capitalistic system of
production, though in many respects very different from
a primitive system without capital, nevertheless resembles the
latter in that labour and land alone (or practically alone) will
share the product.

Such a state, however, would be far from desirable in an
individualistic society based on private property. So far from
disappearing, the gulf between the propertied and the property-
less classes would be well-nigh impassable if land, capitalized
at an extremely low rate of interest, possessed almost infinite
exchange value. Even now, a very large part of what is commonly
called capital and interest is, in reality, land and rent. Think,

CAPITAL ACCLTilLLATION 215

for example, of the colossal increase in site values, especially
in the large towns. Even capital goods proper have their value
increased in so far as the land incorporated in them is now-
re-assessed according to a higher standard of value ; or, as it
is said, because the cost of reproduction has increased. A large
part of apparent annual savings is accounted for by this increase
in the capital value of land and is thus not a real increase in
wealth at all. Monopolies are another source of income of
a similar kind which is not exhausted by increased capital
accumulation, but rather becomes more abundant.

In his work, Om den ekonomtska fordelning och Icriserjia*
(1909), Brock (like Cassel) is sceptical of the possibility of a fall
in the rate of interest, but nevertheless criticizes our analysis of
the consequences of such a fall. According to him, it would occasion
a fall in rents also, since a sufficiently low rate of interest would
render practicable a number of substantial improvements to land
which are now not profitable owing to the lack of cheap capital,
and the supply of land for all productive purposes would become
excessive ; so that the fall in interest would benefit labour
exclusively.

The abstract possibility of this cannot, as we have already
said (see p. 164, n.), be denied; just as, on the other hand, it is
not entirely inconceivable that a fall in interest might benefit
landowners exclusively — ^in so far as the low rate of interest would
mainly lead to the introduction of fixed automatic, or semi-
automatic, machinery, so that human labour would become
superfluous. To what extent the conditions observed by Brock
are of practical importance, however, depends on circumstances
which it is difficult to survey. There is no doubt that many
swamps and much poor soil, not least in Sweden, could, with
an unlimited supply of cheap capital, be converted into fertile
fields. And if the crowding of human beings in the cities could,
with the help of capital, be counteracted (by rapid and cheap
communications by land, water, and air), then site values, which
in certain countries already greatly exceed agricultural rents,
might he lowered — ^though only on the assumption that the
population was reduced or ceased to grow ; otherwise a continued
rise in rents is practically certain — ^and capital might grow, even
relatively to population, to any extent.

Another related question which was much discussed in the
past is the extent to which the unchecked progress of capital

^ [‘* Economic Distnbution and Crises.”]

216

LECTUEES ON POLITICAL ECONOMY

accumulation is of advantage to those who only indirectly profit
by it, and especially to the labourers. The older economists
usually had very exaggerated views on this point, because they
supposed — on the basis of the wage-fund theory — that an increase
or decrease in capital would produce a proportionate increase or
decrease in wages. This, of course, is not the case. A great increase
(or decrease) in capital may doubtless be associated with an
insignificant change in the rates of wages, less in proportion as
there exist opportunities for long-term investment. And since,
in our day, the labourers often do some saving themselves, their
position will, of course, be much better if somewhat higher wages
enable them to save something on their own account than if the
capitalist employers, by paying lower wages, were enabled to

save a corresponding (or even larger) amount on their account.
In the former case they are enabled to reap both the direct and
the indirect profits of capital accumulation ; in the latter case
they have only the indirect profit, which may be very small.

In this connection, we may refer to a celebrated and very
peculiar speculation of the famous German economist, von Thiinen.
He remarks that if the labourers themselves are willing to save and
accumulate capital, then they are best served if wages are neither
too high nor too low ; for if they are too low, their savings will be
insignificant, and if they are too high (in relation to the output of
labour) the profits of capital and consequently the interest on their
own savings will be so small that there will be no inducement to save.

If we call the product of labour p and wages Z, then p — I will
be the employer’s surplus, and interest (for as many years as capital
remains, on the average, engaged in production) will be measured

^7 — y — • The labourer also must be able to count upon the same

interest on his savings. If he consumes the quantity a only and
saves the rest of his wages, then his income from interest on these
savings will clearly be proportionate to ; —

a) (p - 1)

Since p and a are to be regarded as given, this equation will
reach its maximum when the sum of the two negative terms
(on the right-hand side) is as srmll as possible. But these terms
have for every value of Z a constant product ap ; their sum
therefore will be least when they are equal. Thus we obtain -

CAPITAL ACCUMULATION

217

Tids last expression — ^the geometric mean of the workers^ minimum
standard of life (or usual standard) and the total value of the
product of labour — ^is therefore regarded by von Thimen as the
natural wage ” — ^and he wished to have this formula engraved
on his tombstone. We will not pause to criticize it thoroughly.
In any case, the formula must be considerably modified if it is
to correspond with reality. For, in the first place, the rate of

interest is not reduced proportionally to the expression —

when I increases (which would, as will easily be seen, presuppose
a constant period of production), but, as a rule, much more
slowly, owing to the fact that employers react to every increase
in wages by lengthening the period of production (introducing
labour-saving machinery). In the second place, the interest of
the labourer in his savings is not limited to the mere income
which they yield, but includes the saved capital itself ; he saves
for furnishing his house, for his children’s education, for his old
age, and so on. The most advantageous value of I is therefore
probably much nearer p than von Thiinen supposed.

What has been said may suffice to indicate, rather than
to solve, the many problems associated with the question of
capital accumulation — ^which has been so little investigated.
The subject has, however, several further important and
interesting phases which are related to the fact that, in our day,
capital is almost always accumulated in the form of money.
We shall revert to these phases when we deal with the theory
of money.

On the other hand, we must be careful not to forget that
money or credit is only one guise, one form, of capital accumulation.
The amount of hard cash in a country can be neither increased nor
decreased by saving, but remains, on the whole, constant ; and
credit documents of various kinds are at most only titles to material
property, except in so far as they presuppose a destruction of real
capital, as in the case of war-loans, etc. Real, productive, saving
therefore always assumes the form of real capital. In the normal
course of business this process is clearly visible. The commodities
which a person foregoes by saving, and by restricting or postponing
his consumption — or rather the labour and land which would
otherwise have gone to the production of those commodities —
he places directly (or by means of money, credit or credit-
institutions) at the disposal of an entrepreneur who converts
them gradually, as the savings are efiected, into more or less fixed

218 LECTUEES ON POLITICAL ECONOMY

capitel-goods, i.e. real capital. At the close of a boom, paper
credit often seems to make up, in part (though actually it
does not), for the shortage of real capital— and still more in
a period of depression when investment in fixed capital hardly
pays, but savings continue, though perhaps at a slower pace.
The process of capital accumulation is here not a little enigmatic.'
It must continue in some real form, since there is no other ; but
in what ? Further investigation of this question is highly desirable
and would probably throw much light on a field which is still
the darkest in the whole province of economics, namely the
theory of the trade cycle (and of crises). But we cannot consider
ttot subject here since we have, throughout, restricted our
ob^rvations to the economic phenomena of equilibrium in the
ordinary sense to static analysis as distinct from dynamic.

APPENDICES 1

1. Peofessor Cassel’s System of Economics^

(i) Oassel’s refutation of tiie tlieory of value, Ms theory of exchange,

and Ms views on the pricing mechanism.

(ii) The theory of interest, the theory of rent of land and mines,

the theory of wages.

(iii) The nature of money and international pajnnents.

(iv) The theory of trade cycles.

I

Professor Cassel, like so many others, has felt a call to
present his scientific system to a wider public than that wMch
could follow Ms lectures. He has for this purpose secured the
collaboration of Professor L. PoMe, of Leipzig, who is eventually
to publish the preliminary part, dealing with historical and
sociological developments, of their joint work, Lehrlmch def
Allgememen VolksmrtscTiaftshhre. Professor Cassel is the author
of the second and purely theoretical part, wMch is now published
in a large volume.

To review tMs book one must sit in judgment on the whole
of the author’s lifework in the sphere of theory. Professor Cassel
expressly desires that all his writings — even the earliest and least
mature of them — should be regarded as indispensable foundations
for the theoretical edifice, wMch now appears in its completed
form. The wisdom of refraining from a fundamental revision of
Ms earlier, and in my opinion, less completely developed views,
while not letting them fall into oblivion, may perhaps be
questioned. But naturally this is his own concern. For my part
I also have felt the need of arriving at an understanding of Ms
whole approach to theory. On various grounds, mostly personal,
I have never undertaken a public criticism of any of Ms work,

1 The translation of the appendices which fdllow is the work of Mr.

Solomon Adler. , ^ w Tur- ^

2 [This review of CasseFs Theoretische SozidldJconomiet Leipzig, C. F. Winter,
1918 (viii, 582 s.), first appeared in the Bhynomish Tidsknjt, 1919, No. 9, and
was published in German in SchmoUer’s JaJirbw:K 1928, vol. lii-2. No. 5.
Unless otherwise stated, all page references are to the 2nd edition of The
Theory of Social Economy, 1

219

220

LECTURES ON POLITICAL ECONOMY

with the exception of his very first essay in the Tvbinger
Zeitschrift?^ If I delayed much longer, it might be too late for
either or both of us. This may excuse the unusual length of the
following essay.

The many excellent qualities distinguishing Professor Cassel’s
earlier writings and also — I believe — ^his direct teaching activities,
are to be found in abundance in this work. I envy him his ability
to present generally accepted economic doctrines concisely and
comprehensively, and to throw light on them with well-chosen
examples from the world of affairs, with which he appears to
have acquired a practical acquaintance. Last and not least there
is his laudable attempt at a description of concrete economic
phenomena, based on statistical material — ^this being especially
evident in the fourth section of the book, on cyclical fluctuations,
which I hold to be the best.

With these merits, however, Professor Cassel possesses the
defect of desiring at all costs to be esteemed an original and even
path-breaking theorist, and this in every branch of economics.
It remains a riddle how with his diligent activities as a publicist
and with his numerous public duties, he can have found time
for these inquiries, for nothing is so consuming of time as scientific
thought. I am afraid that his claim is based on an illusion. BSs
originality does not extend in most cases beyond an exposition
of the ideas of others in a new, if not always improved, version.
Innovations are generally the mark of an indomitable desire to
pnetrate the obscurer regions of theory ; but this end is not
often achieved by those who have too cursory an acquaintance
with the terrain. The reader finally ends in a bog of mental
confusion, which a facile style can no longer conceal, and from
which the only escap is to revert to precisely that literature
which is here so contemptuously dismissed as ""unnecessary’’
and scholastic

The first and most striking of these tours de force is the
wholesale rejection — ^already apparing on the first page of his
introduction— of "" all the old so-called theory of value Of
course, he means the modem theory of value. He has always
been more amiably dispsed towards the older theories of value ;
this, together with his charm of expsition, was what recom-
mended him to the aged Schaffle.

^ Grwndriss einer elemetUaren Preislehre ( 1899 ).

CASSEL’S SYSTEM OF ECONOMICS 221

On tlie other hand, he wants to extirpate the modem
subjective theory of value ; but he substitutes for the concept
of marginal utility either nothing at all or the ^"principle of
scarcity He asserts that the psychological phenomena lying
behind price do not belong to the economist’s domain. This
idea reminds us of the English stockbroker, who earned his
income, year in year out, by buying and selling railway stock
without knowing where the railway was. He also repeats his
old objection about the impossibility of measuring utility ”,
as though exchange and economic activity in general — even
in a primitive economy — ^would be conceivable, if we could not
estimate the utility of different objects to us. Similarly, the
deliberations of members of Parliament on problems of taxation
would be meaningless, if it were impossible to compare the
utility of the same good to different persons. (It is characteristic
of Professor Cassel that when he has to talk about so-called
collective wants, he dismisses the whole thing as a manifestation
of force ‘‘ Zwang, Zwangswirtschaft, ZwaTigorganisation,^’ et
praeterea nihil.) He hims elf is of the opinion that the “ economist ”
must adhere exclusively to money prices as being a ‘^precise
magnitude ” — and this was written or printed in the last year
of the Great War, when money as a measure of value became
completely bankrupt.

He also maintains that marginal utility as the basis of
exchange value presents the disadvantage that it is neither
given nor determinate, but is itself variable with and dependent
on the prices which it is intended to explain. But how does this
apply to scarcity ? ” A commodity is not scarce because it
is present in small quantities, but, as Professor Cassel himself
states in the Introduction, it is scarce only in relation to wants,
or to the extent that it becomes an object of demand. And the
degree of scarcity is measured in exactly the same way as
marginal utility, by the strength of the next unsatisfied need,
which first causes the 'commodity to be recognized as scarce
In other words, scarcity and marginal utility are fundamentally
one and the same thing ; Walras already recognized this, for
the word “ rarete ” (which he used as an alternative to utilite
finale ”) signifies scarcity as well as rareness.

Such, however, is not Professor Cassel’s opinion. Strangely
enough, he hims elf — ^apart from the above introductory passage —

222 LECTURES ON POUTIOAL ECONOMY

gives no description of the concept of scarcity, otherwise the
relationship might have become clear to him. To compensate
for this omission, he prints in italics the following definition of
the principle of scarcity. “ In the exchange economy,’’ he says,
“ the principle of scarcity signifies the necessity, by the pressure
of prices, to adjust consumption to a relatively scarce supply of
goods ” (p. 74). What is meant by a “ scarce supply ” remains,
as we have said, unexplained. But even so, this definition is
absurd, for there is no need to be afraid of consumption exceeding
supply. In the later coume of the work the word “ consumption ”
is consistently replaced by demand ” in this connection.
And in this formulation one can indeed recognize the principle,
for price undeniably has the "^task” of equating supply and
demand, so that all the supply is sold and no effective demand
remains imsatisfied.

But if the Principle of Scarcity did not contain anything
ehe^ it would be absolutely identical with the ancient principle
of equilibrium between supply and demand, of which Cassel
does not suppose himself to be the discoverer. The doctrine
of marginal utility goes beyond this by stipulating equality or
proportionately between commodity prices and their
“ scarcity ” (= marginal utility) for each exchanging individual.
That this principle is by no means so easily established, ought
to be proved by the fact that, even Gossen, the first expounder
of the theory of marginal utility, did not reach it. That it was
not unnecessary ”, seems to follow from the fact that not less
than three genuinely path-breaking scientists advanced it as an
important discovery at roughly the same time. Certainly it
contains nothing absolutely new, but neither did the discovery
of the differential calculus ; the service of both consists in their
having replaced diffuse or imsystematic ideas by a clear general
concept and, what is no less important, by an adequate
formulation of it.

Why has Professor Cassel absolved hiifiself from this task ?
Why, apart from an otherwise perfectly correct resum4 in a few
lines, has he withheld from his readers this serviceable guide
through the labyrinth of the theory of exchange ? For example,
the concept of elasticity of demand with falling and rising prices
becomes much clearer, if it is based on the elementary principle
that marginal utility always remains proportional to price. Here

223

CASSEL’S SYSTEM OF ECONOMICS

also Professor Cassel advances without closer examination
a series of statements, of wMch a few are correct, but generally
require an explanation, while others are doubtful or completely
wrong ; such as the statement (p. 80) that demand must
invariably rise with a fall in price, and mce versa. This is not
certain in the case of goods which are partly substitutable in
consumption, and in the case of the reservation demand of the
holders of the goods themselves. The effect on the latter of
a rise in the price of their goods may quite conceivably be such
that they retain a greater proportion for their own use. This
must have been the case to a great extent, if I am not mistaken,
with those who produced for their own needs during the war.
Professor Cassel himself gives an extremely brief account of
the fundamental concept of marginal utility, and it would not
surprise me, if his readers, so far from thinking this account
“ unnecessary were, like Oliver Twist, to ask for more.

Another peculiarity of Professor Cbssel’s to which we have
elsewhere drawn attention, and which, remarkably enough, he
regards as a step forward, is his use of money as a scale of
reckoning’’.^ He boldly maintains that when the classical
economists attempted, wherever possible, to abstract from the
use of money in their mqumes into economic phenomena, this
was due to their preconception (which according to Professor
Cassel is false) that in primitive society no money was used.
This statement is characterized by a naivete which one would
hardly have attributed to Professor CasseL On the contrary,
this conscious abstraction from the functions of money — ^the
conception of trade, external as well as internal, as consisting
in the last analysis in the exchange of commodities, of capital
as real capital instead of as a sum of money,® of wages as real
wages — ^was the decisive step which first gave economics a truly
scientific character, and first raised it above the hazy and
incoherent ideas of Mercantilism.

For the rest, Professor Cassel does not succeed in carrying
his method through consistently. In his treatment of the
pricing mechanism ”, to which we shall later return, he first

^ Cf. his “ Gnindriss ”, where he tries to base the whole of economics on
the useful “ fiction ” that a shilling has the same economic significance for all
men, whatever their economic position.

* Later on. Professor Cassel has to “ warn ” his readers against confusing
real capital and money.

224 LECTURES ON POLITICAL ECONOMY

assumes that each consumer h^ a certain purchasing power
(expressed in money), and he naturally arrives at the result
that the prices of commodities will be completely determinate.
I became vastly interested in reading this, for I thought that
the next step would be an attempt to demonstrate how this
monetary purchasing power arose and was maintained. But
nothing comes of it. The hypothesis is merely advanced only
to be dropped later, and quite unexpectedly the explanation
follows that the phenomena of exchange and production only
suffice to account for relative commodity prices, but not absolute
money prices, a task which must be kept in reserve for the
theory of money as such. Now it should be noticed that Cassel
explicitly says that at this stage he will consider money
eocclicsively as a ‘‘ scale of reckoning ”, and will thus provisionally
abstract from its function as a medium of exchange, which
perhaps may even be taken over by some other commodity —
as in Homer’s times, when “ oxen ” were used as a measure
of value, although they hardly constituted a general medium
of exchange. In this case, however, money would retain its
character as a commodity perfectly intact, and the use of money
as a measure of value would not prejudice it in the least. In
other words, the exchange value of money would be determined
by the phenomena of production and exchange in exactly the
same way as that of other commodities, and ex hypothesi the
prices of commodities expressed in money would be uniquely
determined precisely by the ‘‘ pricing mechanism ”, and not
merely, as Jftofessor Cassel states, prices multiplied by any
factor whatsoever ”. Further, we should get the same result,
if money were, strictly speaking, nothing more than a medium
of exchange, i.e. the means of presenting goods on the market.
For an amount of money, however small, can, as we know from
experience, effect the exchange of any quantity of commodities
whatsoever. Now money has also a third function, which is in
practice the most important, i.e. as a ‘‘ store of value ” a reserve
or cash balance. It is through this characteristic that with given
commodity prices the need for a certain amount of money obtains,
and it is here that the amount of money becomes a factor of the
first order for commodity prices. Further, it is through this
property that the character of money as a commodity recedes
into the background, becomes secondary, or even vanishes

225

CASSEL’S SYSTEM OF ECONOfflCS

altogether. THs was perfectly clear to Walras ; he first treated
money as numeraire ” (imit of account) and only later as
“ monnaie (medium of exchange) ; as far as its first property
is concerned, it is for him only one commodity among many.
Professor Cassel, on the other hand, argues as though the oxen
of Homer were not generally the object of consumption and
exchange, but only served as a ‘‘ scale of reckoning Here at
least the premature introduction of money has contributed not
to increased lucidity but rather the reverse.

A more valuable element in Professor CasseFs account is
the emphasis laid on the reciprocal relationship between products
and the factors of production in the pricing process. In those
of his earlier writings which I regard as his best,^ Professor Cassel
has shown with a masterly clarity that as soon as we have more
than one factor of production (e.g. simple manual labour), and in
fact we have hundreds of different kinds, the principle that costs
of production determine the exchange value of a product can no
longer be maintained. These costs become quite simply the
prices of the factors of production, which are necessarily
determined in combination with the prices of commodities in
a single system of simultaneous equations. TMs idea, however,
belongs to Walras ; it is his powerful sjmthesis which in the
last analysis lies at the basis of Professor CasseFs ‘‘pricing
mechanism Professor CasseFs indebtedness to him is obviously
very great, but instead of showing the gratitude he ought to have
expressed, he does not mention Walras’ name once in the whole
book.2 He adheres, though not altogether consistently, to the
principle of never quoting anybody but himself. He has not,
however, accomplished any improvement in Walras’ exposition
— apart from a certain simplification in the formulae. On the
contrary, he breaks off in the middle, with a resulting loss in
coherence. Following Walras, he describes how the total rewards
of the factors of production are in the main identical with total
(real) incomes, and are at the same time the source of the demand
for goods and services ; he adds that these incomes are not all

^ Die ProduHicmskosUTiiheorie Bicardos, etc. (Tubinger Zeitschrift,
1901). In this well- written essay he also pays to the theory of marginad
utility a tribute for which one looks in vain in his other writings.

* In his “ Grundriss ”, he explicitly bases himself on Walras ; but only
a couple of years later be describes his own essay as the first attempt ” of
its kind ! {Der AusgangsfunM der theoretischen Oekonomie, Tubinger Zeit-
schrift, 1902, p. 0971)

Q

226 LECTURES ON POLITICAL ECONOMY

consumed, but are partly saved. But at this point the equality
(wMch. we bad previously accepted) between tbe sum of tbe
factors of production now available, and that part of them which
enters into the various goods demanded for consumption, ceases
to obtain, and Professor CassePs system of equations (7) (p. 144)
is no longer valid. For the whole system to function, it is not only
necessary that the savers, as Professor Cassel assumes, should
decide how much to save on the basis of ruling prices or in
relation to the determination of prices, but also that they, or the
entrepreneurs in their stead, should be clearly aware what
factors of production to demand in order to invest their savings
most profitably. Of this, Professor Cassel says not a word.
But even if the reader in distress could fill this gap unaided,
he would in any case begin to have doubts, when, in the course
of the book he meets Professor CasseFs factor of production
capital-disposal ’’ and its ‘‘price’’, interest, and tries to
accommodate these magnitudes with the other factors of
production and the prices in the formulse previously given. It
would have been of great interest if Professor Cassel had
indicated how this could be managed without double
reckoning.

Walras proceeds in an entirely difierent manner. For him
the capital-^oods themselves are factors of production ]ust as
much as labour and the forces of nature ; and the rate of interest
“ le taux du revenu net ” is considered as the ratio between the
expected yield of the capital-goods now being made (= the price
for their factors of production minus the necessary amortization
costs) and their own cost of production according to present
prices. Thus it here represents a-“ parameter ” in the “ functions ”
which determine saving. Savers and entrepreneurs strive to
maximize this ratio, and equilibrium is reached when it is the
same for all alike. In this way Walras constructs an extraordinarily
coherent and rigorous system, which, when it is combined with
the systems of J evons and Bohm-Bawerk, both completes and is
completed by them.^ Professor Cassel simply omits the whole

^ Clearly Walras’ method does not yield the actual rate of interest which
the future reveals, but the anticipated interest on which the level of the loan
rate is directly dependent at any moment of time. At this point I must with-
draw an objection which I previously made against Walras— i.e. that his
theoiy of interest necessarily presupposes a progressive type of society. Walras
indeed said so himself, but the truth of the matter is that it is just as applicable

227

CASSEL’S SYSTEM OF ECOKOmCS

of tMs vital section of Walras’ system, and defers tlie theory of
capital to the next book, when he moves more freely without
having to trouble himself about algebraical formnlse. But more
of this later.

We are now confronted with the difficult task of giving an
account of another peculiarity in Professor Gassei’s presentation
of fundamentals. It is well Imown that the classical economists
were often inclined to adopt a method of approach in which
they regarded free competition or a free pricing mechanism
as a kind of moral factor — an economic providence, so to speak,
which gave each participant in total production his allotted and
just share of the product and, at the same time, gave the
maximum sum of satisfactions to all. Among contemporary
economists, Professor Cassel should be one of the last to find it
easy to escape from this approach. It is true he does not go so
far as to make the existing state of society, based in principle
as it is on free competition, the ideal of social justice ; Ms own
parable ‘‘ of the bread of the poor wMch is sometimes thrown
to the dogs of the rich ” bears evidence of this. But essentially
he stands by the classical system. He emphasizes as often as
possible its economic superiority, and if he can do nothing else
he praises “the free ^choice of consumption goods” wMch it
provides in contrast with, for example, a similar socialist state.
He is so little afraid of provoking laughter that in another context
he adduces salt and ink as proof of the fact that even the poorest
can almost completely satisfy some of their needs.

Actually the lower classes in present-day society do not
in the least possess free choice in consumption ; as far as means
of subsistence proper are concerned, they are allotted all the
cheapest brands, and their remaining consumption is similarly
organized. A compulsory rationing of the most important
commodities, as in war time, would certainly give them greater
freedom in their “ choice of consumption-goods

When we are dealiug with production apart from distribution,
we can then say that, in a certain sense, economic freedom

to the stationary state, and in fact gains thereby in rigour. The underlying
assumption is that the factors of production will have the same relative values
or prices in the future as they have at the present moment. Actually this is
true for the stationary state, but it does not hold for the progressive economy,
unless we postulate a uniform increase m production, which is stnctly speaking
inconceivable, as the sum of natural forces cannot be increased.

228 LECTURES ON POLITICAL ECONOMY

promotes ‘‘economy”, for as soon as a surplus of exchange
value can be obtained at any point with the available factors
of production, under free competition they are necessarily
transferred to that point. Yet we must of course remember
that the hind of production is determined by effective demand,
and not by the socially desirable demand for products — ^two
concepts which Professor Cassel is only too inclined unconsciously
to confuse. The problem of the share of the factors of production
in the resulting total product is, in the last analysis, identical
with that of social distribution, and no eloquence can conceal
the fact that “ the Principle of Scarcity ” only produces a hare
mechanical levelling, which faide de mieux may perhaps be
preferred to any other, but which is not based on any ethical
or sociological principle. The “ simultaneous equations ” are no
guarantee that any “ variable ” cannot assume the value nil,
even if we are discussing so important a social factor as wages,
or so questionable — ^not to say odious — a social factor as the
rent of land, site-rent, or certain monopoly revenue, etc.^

The situation is worsened if free competition is abolished
by agreements, and the contracting parties are ranged against
each other like two opposing armies, for here in most cases
the result is at least as uncertain as that of war in general,
and mutual destruction is the only outcome of which we can
be sure.

In an extremely well-written section, xiv, which is, however,
too optimistic and “apologetic” in tone. Professor Cassel
himself gives a vivid description of the tendency towards an
ever-stronger limitation of freedom of production which
characterizes modern economic development. But even here
he seeks, wherever possible, to defend his suum caique. He
wishes us to believe that when large-scale enterprises agree to
form trusts, it is because they would otherwise have been forced
by internecine competition to produce at a loss. And he points
out that when the State is compelled to grant monopolistic
powers to certain corporations such as railway companies, it
seeks to limit the pernicious utilization of this monopoly by

" In “ Der Ausgangspunkt, etc.,” Cassel is so raclical that he wishes to
confiscate all ground-rent proper (p. 6S6) ; in the present work he arrives at the
surprising conclusion that urban site rents are “ essentially the result of man’s
productive activity ”, It is not stated how this should be taken, and what
conclusion he infers.

229

CASSEL’S SYSTEM OF ECONOMICS

maximum rates and the like . Moreover the monopolist is sooner or
later threatened by latent competition, for example, from abroad.

Here it should be noted that a monopolistic system of prices
is by no means the worst ; if we assume that there is only one or
at most a few monopolies in the whole market. If, however,
many branches of production become monopolized or trustifxed, it
would ultimately become aimless for them to raise their prices
against each other; they would have to seek their profit —
apart from a certain technical advantage lying in combination
— in more or less common action by which the prices of those
factors of production not in their own possession (and especially
the wages of labour) would be forced down, or at least be prevented
from rising. The State has not, at least up to the present, been
in a position to react against this procedure.

This vagueness in Professor CasseFs social views is analogous
to a similar vagueness in his theory. Although in Ms own system
there are no independent costs of production but only prices
for the different factors of production (which equal their share
in the total product), he considers it important to mention that
the price of each good must coincide with its costs of production
— wMch on Ms assumption becomes merely a platitude, a self-
evident fact (in so far as the costs of production can be imputed).
In other words, each demand must carry the costs bound up
with it,’’ or, as Professor Cassel sometimes expresses it, without
further classification of the concept, it must carry the necessary
costs All tMs is hopelessly obscure ; perhaps it is Walras’
principle of the tendency of entrepreneurial profits to zero, of
wMch originally he had a glimmering. But later it seems to
have escaped Ms attention, that it holds only under perfect
competition, and that certain costs ”, wMch even
in perfect competition are economically necessary, are not
therefore socially necessary. A division of the yield of land
among the consumers of food or the yield of forests among
the consumers of timber on a pro rata or some other basis would
not indeed lead to a fall in the price of tMs commodity, but it
would lead to a fall in the actual expenditure on it.^

^ Apart from its application to the rent of land, the first statement of this
view of Cassel’s is to be found in his essay “ Ber Ausgangspunkt, etc.,*’ an
essay which in my judgment is extremely obscure and completely mistaken in
its results, and with the shortcomings of which Cassel is not yet sufficiently
acquainted. In the present work Cassel has somewhat modified the

230 LECTURES ON POLITICAL ECONOMY

In order 'to state ” or produce ’ — wHcliever word we

prefer — ^tMs equaKty between costs and the prices of commodities,
tbe '' Principle of Scarcity according to Professor Cassel, is no
longer sufficient. In many places there is some indeterminateness
in costs of production, to overcome wMch no less than four
extra supplementary principles are in his opinion necessary.
These he calls the DifferefrUial Principle, the Principle of Decreasing
Average Costs, the Principle of Substitution, and finally the
Principle of Joint-products. They are four too many. The last
may have some significance, but rather as an exception to the
Principle of Costs ’’ than as a means of establishing it. If two
or more products are technically combined in production in
a constant technical proportion, then an imputation of their
costs is out of the question, whereas naturally each has its
particular market price determined by supply and demand. If,
however, which is more usually the case, the technical proportion
varies (sheep for mutton or wool respectively, etc.) particular
costs exist at the margin of production, and these must coincide
with their price in the usual way. The same holds for the
Principle of Substitution. On the whole the different factors
of production are not wholly substitutable, but are simultaneously
applied. At the margin of production, however, a contemplated
(virtual) increase or decrease in any one of them can be regarded
as its economic contribution, and this is necessarily proportional
to its price. But this substitution value, or, what comes to the
same thing, this marginal productivity is measured in the same way
as the “ scarcity ” of the good, with which it is thus identical if it is
correctly defined. Professor Gassers reiterations to the contrary
are, in my opinion, merely evidence of an incomplete analysis.

Neither is the Differential Principle an extraneous addition
to the Principle of Scarcity ; here it is essentially a question
of different factors of production, each of which in spite of an
external similarity has its own scarcity and price. Two pieces
of land of different fertility or at different distances from the
market are not the same thing, even though they may appear to be .

statements he there advanced ; for example, he no longer e.g calls for a
fee-principU, where it can be generally applied, which shall be the only
right one for the financing of public enterprises. But he still strongly mclmes
to this opinion, and in a discussion in the Natwnalekonomisk Forening (Economic
Club) he curtly opposed every other kmd of “cover” for State railways, for
no reason whatsoever.

CASSEL'S SYSTEM OF SCONOinCS 231

But most suspicious and to me most incoinpreliensible is
the Principle of Decreasing Costs Professor Cassel in Ms
introductory remarks on tMs subject extending ovet several
pages, maintains that as lie has already treated the position
of different firms in relation to each other (under the Differential
Principle he will now assume for the sake of simplicity that
each commodity is produced by only one large firm. Even so,
costs of production can in his opinion be indeterminate, in so far
as they vary with the size of the firm. If costs increase as the
firm increases, the case is simple (he says) — it is the highest
costs, i.e. the marginal costs, which determine price. He says
nothing about the destination of the profit in such a case, but
suddenly abandons the whole of this interesting special question.
And it is just as well, for it is dijficult to imagine a large firm
with increasing costs of production. If production on a small
scale is more remunerative than on a large, factory work gives
way to domestic work, large property is parcelled out into
smallholdings, etc.

On the contrary, the large firm with decreasing costs (as the
firm’s scope extends) is an actual fact. Here, says Professor Cassel,
the highest costs cannot be price-determining, as ‘‘ they are at
the bottom and not at the peak of production But neither
can the price of the good be equal to its marginal costs, for the
firm could not then maintain itself. Consequently, he concludes
that we must choose the via Tnedia, where the price is determined
in such a way that it just covers the average costs, so that there
is no profit for the entrepreneur — ^in contradistinction to the
previous case ! Professor Cassel gives no clue to the entrepreneur’s
reasons for such benevolent behaviour. He goes on to show —
and it is not difficult — ^that in this case ‘‘ at least two ” prices
must exist, a Mgher and a lower, with each of which the firm’s
expenses would be covered. From these he decides that it is the
lower wMoh is chosen ! He first takes the case where the relation
of sales to price varies in such a way that, within limits, production
just pays its way with any price — presumably in order to make
this conclusion more palatable to the sceptical reader. Here we
must admit the producer has no incentive to fix the price Mgher
than is reconcilable with the consumer’s interest. But what of
all the other cases ? Between the maximum and minimum
prices there lies a whole series of prices wHch would yield a

232 LECTURES ON POLITICAL ECONOMY

surplus profit for the producer. Theii why does he not choose
one of them ? If we aasume that he alone is master of the
situation, he will certainly fix on that price which will yield the
fmodmum profit; if, on the other hand, he has competitors,
even though they be smaller and weaker, he presumably chooses
a somewhat lower price in order to ruin them, after which he
can again raise his price. In other words, when the law of
“ increasing returns ’’ holds for a firm, and holds for any expansion
whateoever, then free competition is impossible, and the profits
of the entrepreneur, which finally become a monopoly gain, have
no tendency to disappear.

The astonishing thing is that Professor Cassel is actually
very well aware of this, and mentions it in the very next
paragraph (p. 129). Nevertheless, he later appeals without
further ado to this peculiar “ supplementary principle ” in his
chapter on ‘Hhe pricing-mechanism” (pp. 161 It remains
a puzzle how all tibis can be understood.

The confusion increases when the author, with reference to
these principles ” (p. Ill), applies the expression ‘‘ increasing ”
and ‘‘ d im i nishin g returns ” in an entirely different sense, i.e. as
the result occurring when one factor of production is combined
in increasing quantities with another which remains constant —
for example, when a fertilizer or an increased amount of labour is
applied to land of a given quality. Here there is no question of
an increase in the scale of production ! The principle remains
the same, whatever the area of the land employed. It is true,
as he observes, that an increase in the scale of production
often occurs together with a change in the proportion of factors
employed or is even conditioned by it. This naturally complicates
the problem, but should not lead to a confusion of fundamentally
different concepts.

The whole of this farrago— I can scarcely call it anything
else— is largely to be attributed to the fact that Professor Cassel
stubbornly passes over the earlier specialist literature on this
subject, which he ostensibly finds superfluous ” since the
appearance of his own book.

Amongst minor points in the first book we may only mention
that he (p. 52) includes trade marks and patent rights ” as
part of the total capital ” of a “ closed exchange economy ”
(expressly as “ real capital ”} ; and if I understand him aright,

CASSELS SYSTS^I 0? SC0X05IICS 233

lie includes the increase in the value of land and sites cccurring
during the year in total income (p- 57). Xeither can he
right. An invention, i.e. a certain method of work, has nothing
in common with real capital (though it may well have cost
a large sum of capital), and when a patent expires, society is
none the poorer, if anyt-hing it is richer — otherwise why should
legislation restrict patent rights ? Again, mere increase in land
values may certainly be included in the national income from
a fiscal point of view, but hardly from any other. Professor Cassel
merely says that the national income su^ces to pay for the rise
in land values (which he calls an important principle), but vague
terminology does not improve the matter, nor does it render
it more intelligible. Why not clarify important social relation-
ships instead of obscuring them 1

II

In the second book, the chapter on interest should arouse
mixed feelings in most readers acquainted with the subject,
and this as much for its critical as for its constructive
contributions. The wage-fund theory is categorically described
as ‘‘ sterile dogmatism ’’ — ^it was at least of some use, and the
error in the older version consisted above all in regarding the
fund without further proof as a fund stored up for a single year.
It was this error which led even Eicardo to certain fallacious con-
clusions. But this defect has been remedied in more recent times
by the analysis of Jevons and still more by that of Bohm-Bawerk.

I doubt whether Professor CJassel has the support of any
serious economist when he describes the work of Bohm-Bawerk
(and Menger) as a definite retrogression ”(p. 191) — except in the
sense that they actually went back ’’ to the original ground of
the whole phenomenon of interest (i.e. the exchange of present
against future advantages). It is in this way that their theory
can embrace all kinds of interest, even the case in which no
capital is accumulated in the physical sense, as in consumption-
loans ^ ; most other theories of interest are narrower in this

1 Professor Cassei “ prefers to regard consumption-loans as “ negative
capital accumulation ” from the borrowers^ point of view. Socially or physically,
however, there is no negative accumulation of capital, only an uncompleted
positive accumulation, by which some existmg capital goods are destroyed of
themselves, and the stock of social capital is thus d im i n i s hed.

234 LECTUEES ON POLITICAL ECONOMY

respect. The discourtesy of Professor CasseFs judgment ^ is
even more offensive than it is absurd, Bohm-Bawerk, in his
Geschichte und Kritih, without altogether approving of Senior’s
theory of interest (which stands in the closest agreement with
Professor CasseFs) declares it to be ^‘incomparably superior
to his predece^ors’ theories in its profundity, its system, and
scientific seriousness ”, and defends it against unjustified attacks.
One has only to compare this treatment of so distinguished an
economist as Senior with Professor CasseFs remark on Bohm-
Bawerk in order to appreciate on which side “ sober scholarship ”
is to be found. And since it is clear that Professor Cassel, like
others, takes most of what he really knows about the functions
of capital and interest from Bohm-Bawerk, one involuntarily
recalls the words with which Dr. J. Bonar, for the most part in
good will, concluded his review of the “Nature and Necessity of
Interest ” ; “ Maledicti, qui ante nos nostra dixerunt / ” ^

Jevons’ theory of interest, which is essentially identical with
Bohm-Bawerk’s, is nevertheless called an “ important advance
Professor CasseFs first objection against it is that capitalistic
production does not require “an accumulated stock of
foodstuffs ”, Did Jevons make any such assertion ? Jevons
says that capital in its “ free ” form, i.e. at the beginning as
well as at the end of its existence as (invested) capital, assumes
the form of means of subsistence ; but that is not to say that
this disinvestment must occur en masse and at one blow in any
particular enterprise. I shall return when reviewing Professor
CasseFs own construction to another objection he makes against
Jevons. A third objection is that Jevons “ wishes to determine
interest” exclusively “by means of the marginal productivity
of the extension of the period of production ”, which “ completely
loses sight of the Principle of Scarcity ”, As we have shown,
scarcity and marginal productivity, correctly understood, are
one and the same thing. If we consider capitalistic production
in society as a whole, it consists in the application of the annual
endowment ” (to use a felicitous term of Bohm-Bawerk’s)
to preparing for a consumption, which, on the average, lies at
some point in the future, and at a point more remote, the more

^ Hi® objection that “ some saying would take place even with a zero
rate of interest ” is ludicrous in this context ; if there is no rate of interest,
there is no need for any explanation.

® Economic Journal, 1904.

CASSELLS SYSTEM OF ECONOMICS

235

intensively capitalistic production is. Here the duration of the
capital-investment is the only variable dimension, and an increase
in the social capital is thus ipso facto equivalent to a lengthening
of the average investment-period. It is of course assumed that
the original factors of production, land and labour, remain
constant, or, which amounts to the same thing, that capital
increases relatively to them. Professor CasseFs reference to
‘‘ conservative agriculture where an increase in capital need
not bring about any change in the period of production but at
most an extension of the area under cultivation, is therefore
only an argumentum ad ignoriantiam — ^how far it is ex ignoriantia
it is for the reader to say.

We return once more to Bohm-Bawerk. Of his magnum
opus Kapital und Kapitalzins ”, Professor Cassel says that in
spite of the solid and extraordinarily careful work put into it,
it is in the main misdirected, both in its critical and historical
and in its constructive parts Bohm-Bawerk’s critical mono-
graph, a work without peer in economic literature, which clearly
and decisively demonstrates ^ the obtuseness, superficiality, and
error so characteristic of most of the older attempts to explain
interest — can it be ‘‘ in the main misdirected ” ? Perhaps for
a change. Professor Cassel will enlighten us as to why his own
loud praises of Turgot's theory of interest (in his Nature and
Necessity of Interest ”) are now suddenly silenced.^ But he may
well rejoice that his own youthfuljew d' esprit, the idea of identifying
interest and the quota of capital accumulation for the splendid
reason that they are both proportional to capital as well as to
time,^ escaped Bohm-Bawerk's critical attention. As far as the
Positive Theory ” is concerned, its “ misdirected character ”
should, according to Professor Cassel, already be made evident
by Bohm-Bawerk's ‘"statement of the problem”. “Does the

^ It is easy to explain, as Professor Cassel does ex paste facto, that the
older attempts must be allowed “ to lapse into oblivion ” (p. 185), but it would
certainly not have been so before Bohm-Bawerk had written.

* But we can still find a faint echo of them in his statement (p. 51) that a
piece of land in part yields a certain return, and in part “ obviously ” has a
certam capital value. Actually that is so, but it only becomes “ obvious ’* with
a rational theory of interest-~i.e. one opposed to Turgot’s.

* “ Bas Recht auf den vollen Arbeitsertrag,” p. 124 ff. There Cassel, in
bis eagerness to obtain fairly plausible figures, makes an arithmetical blunder,
which as a teacher of mathematics he would scarcely have excused in his pupils.
When the book appeared I privately drew his attention to this serious error ;
but this circumstance did not prevent him from later quoting his work without
any quahfication, as if no exception could be taken to it.

236

LECTUSSS ON POLITICAL ECONOMY

value of the produce depend on the value of the factors of
production, or, contrariwise, does the value of the factors of
production depend on the value of the product ? Professor
Cassel does not advert to the fact that this well-founded question
was put in exactly the same form by Walras, and that it was
answered, as far as I can see, by both thinkers in exactly the
same way (which is the way Professor Cassel answers it himself).
The question as such makes him uncomfortable. Moreover, he
repeats the same remark against Jevons, notwithstanding his
previous description of Jevons' theory as a “great advance ''J
Can then “ a great advance " be “ in the main misdirected ? ”

I shall not linger long over Professor CasseFs own positive
cbntribution to the theory of capital. Discussions in this sphere
are only too easily lost in a maze of words. Eor my part I cannot
feel myself bound to any particular terminology, but have often
declared that as long as the time-element is given its appropriate
place, the starting-point for the construction of a theory of
interest can be chosen almost at random ; it does not really
matter whether we start from the productivity theory, or from
use, or abstinence, or even from the theory of money. The
only important thing is to be consistent. But it is just this
consistency that I find wanting here. We can eitheT adopt Walras’
method of takiiig a cfoss-section through social production at
a moment of time, and thus consider only the co-operation of
the factors of production existing at the moment. In this case,
no doubt, the demand for finished products constitutes an
indirect demand for raw materials and the factors of production,
by means of which the finished products are produced. At the
same time there is a demand for new capital-goods, and their
present yield is the basis for their estimated future yield. We
thus gain a clear insight into the mechanism by which loan-
interest is determined at each moment of time. In this method

^ Ttat Bohm-Bawerk’s work does not lack faults, and that he did not give
us all that he could have given under more favourable circumstances, is my
opinion too. When my book, Uber Werty Kapital und Rente appeared, Bohm-
Bawerk wrote me that the objections I there made agamst his theory coincided
at many points with the “ self-criticism ” he never ceased to exercise on his
own work. One might infer that he had in mind a further development and
completion of this system. But nothing came of it. Por many years his time
was claimed by political activities, and also he later found himself the object
of so many (more or less) unwarranted attacks that m the end it became a
point of honour to reprint his work practically unchanged even in the last
edition.

CASSEL’S SYSTEM OE SCOXOSHCS

of procedure we liave no use for “waiting as a factor of
production ” (thougli it enters to some extent as tiie regulator
of saving). Or else we can refer eveiytiiing back to the original
factors of production in conjunction with waiting (or preferably
iiriie)» Here we make a hn^itudinal section instead, and
this construction is also admissible. Tliis iongitudinai section,
as Professor Cassel does indeed remark, actually extends
indefinitely in time in botb. directions. Tins indefiniteness,
nowever, is of no practical importance, since the major portion
lies between finite limits. If we proceed thus, the indirect demand
for the factors of production from the consumers' side becomes
a mere metaphor, and we also cease to take capital-goods into
consideration ; adopting the scheme of Jevons and Bohm-Ba werk,
everything is resolved into a continuous production directed
towards the future.

In the first place, this method gives us a purely theoretical
insight into the very origin of interest ; but practically, as
I observed in my Uber Wert^ it has the serious drawback, which
arises from the durability of certain capital investments, of
presenting the process of successive readjustments, from which
an equilibrium situation would ensue, as embracing an interval
of time where centuries are the merest episodes. This incon-
venience, however, hes in the very nature of the subject-matter
and cannot be avoided. For practical purposes we might of
course confine our attention to shorter periods, and put
particularly durable capital-goods in a group on their own as
a kind of “ Eentengiiter ” — comparable to “land” and the
supply of natural forces. This procedure I there proposed and
it is this which Professor Cassel now adopts, but of course we
do not obtain more than a provisional equilibrium situation
in this way.

Professor Cassel oscillates between these views without
giving any precision to the concepts he uses. In the section
on the pricing-mechanism, he would also like to restrict himself
to the given moment. But on page 207 he says that “any
analysis of the exchange-economy must be limited to a fairly
small and determinate period ”, Here it is therefore not
a moment of time but a 'period of time that is still being dealt
with, and we are not told how its duration is to he determined.
A few pages later (p. 215) he adds that “ the connection

238 LECTUEES ON POLITICAL ECONOMY

appears most clearly if we regard the services (of durable
capital-goods) as the ultimate products and thus include waiting
for their services in the production process in its wider sense ”,
etc. Here, therefore, we must necessarily deal with a significantly
long ‘‘period”. * Yet he makes no attempt to complete his
previous “ equilibrium equations ” by taking account of this
omission, and the cardinal question of whether the “ price for
waiting” (interest) is determined by its own scarcity or the
“ scarcity of capital ” remains shrouded in darkness. The
problem is indeed difficult ; it is only Professor Cassel’s claim
that he has made it so much easier than his predecessors that
gave occasion to these reflections.

Professor Cassel’s favourite expression “capital-disposal”
(it used to be called Kapitalrmtzung or the use of capital) is not
particularly suited to the clearing up of the matter. This
“ capital-disposal ” soon becomes synonymous with waiting (m
which case it is superfluous as a term), and then a condition for
waiting (and therefore not synonymous with it) in the waiter him-
self and later we take it to be the waiter who puts his capital
at the disposal of another. “ Waiting,” we read (p. 199), “ implies
that a person foregoes for a time the disposal of capital.
Capital-disposal is the right of disposal over capital thus
rendered possible for this period.” ^ But what is the word
“ capital ” doing here ? The man who saves and waits certainly
foregoes the consumption of some of his income, and eventually
places this income at another's disposal in exchange for a future
(greater) income. A house costs £5,000. I have an
income of £1,000 per annum plus 95 shares of £50
each, and either get the house built or want to buy it. I forego
the consumption of a quarter of my income, or £250, and
sell my shares in lots of £250 to nineteen other similarly
situated persons, each of whom saves a quarter of his income
in order to obtain possession of the shares, which thus only
change hands. (Alternatively, they might have taken out
mortgages on the house.) With these twenty parts of twenty
different persons' incomes the house is paid for, and no house

“ In order to be in a position to take over this function (waiting), we must
dispose of a certain amount of capital m the abstract sense ” (p. 199). The
words “ in the abstract sense ” admit of no explanation, for nowhere previously
has th^e been any defimtion of capital other than real capital.

® The italics are mine.

CASSEL’S SYSTEM OF ECONOMICS

239

has ever been built or purchased in any other way when pajrment
was made in cash. The builders of the house obtain a new income,
which they can dispose of as they think fit. The matter is just
as simple in practice. Why make it more complex purely for
the sake of jargon ? Professor Cassel also has a predilection
for the phrase “ capital-market ”, but fundamentally it is only a
metaphor, for no capital in the physical sense is either demanded
or supplied on this market, but simply and solely portions of
income, which are supplied by savers and demanded by
entrepreneurs.

Characteristic of Professor Cassel is his sharp distinction
between durable goods and consumption goods. Here also he
must have been primarily inspired by Walras, who as we know
defined the former exclusively as capital and the latter as
‘‘ revenus ” ; for the simple reason that the total value of the
future services of a durable good is as a rule greater than its
present value, the difference constituting interest. This
distinction, however, cannot be justified. Even the goods
which are consumed in a single act must be counted as capital
when the act of consumption occurs in the future and the goods
obtain a greater value through the very act of waiting. Broadly
speaking, the manufacturers’ and merchants’ stocks of raw
materials and finished goods belong to this category, as Professor
Cassel himself admits, although he is apparently inclined to
belittle their importance.^

None the less he wishes to maintain without qualification
that this distinction is essential. Even in the Introduction he

^ Whether stocks of such goods arising from the intermittent nature of
production should be included in the capital concept is a detail of mainly
theoretical interest. The answer to the question is in the negative. Professor
Cassel attempts to show that the need of an economic distribution of the
consumption of such a stock, e.g. the stock of wheat until the next harvest,
would of itself produce interest (p. 216 n.). But he succeeds in showing some-
thing entirely different, i.e. that if money interest originated in another way,
the price of wheat during the consumption-year must successively rise. Here
it is precisely the rate of interest which brings about an increasing inequality
in the consumption of the stock of com, whereas accordmg to Professor Cassel
the function of interest should be the reverse. The explanation should be
simply that the scarcity of the stock has no effect on the height of the rate of
interest. If everything is completed in terms of com there is no rate of mterest
even in Cassel’s example, and if wheat were the only commodity produced, it
it is difficult to imagme how transactions within the harvest-year could produce
interest. But not so when they are extended from one harvest-year to another,
when the rate of mterest would be a symbol of the discontinuity of production
itself.

240 LECTUEES ON POLITICAL ECONOMY

devotes to the subject space and attention wMcb seem to me
to be wasted. Again, when lie is explaining the origin of interest,
lie clearly distinguisiies between “ the gradual wearing-out
of durable goods ” and “ time-consuming production in the
real sense and be accuses (p. 194) Jevons (and B5hm-Bawerk)
of “artificial constructions’’, when they try to “force” both,
processes “into a single form”. We may well admit that tbe
technical aim of capitalistic production is, or at least can be,
different in both these cases. One or more time-intervals can
deliberately be mserted in production in the latter, mainly in
order to utilize tbe free forces of nature (tbe storing of wine
in cellars, the effects of sunlight on vegetation, etc.). With durable
goods, however, it is largely a question of joint supply. A capital-
good is given durability in order that it should yield more
services, but these must, on the average, necessarily be postponed
to a more or less remote future. From an economic point of
view the difference is therefore unessential — ^the less so because
increased durability often goes hand in hand with an all-round
increase in efficiency ; and it entirely disappears if, as in other
cases of joint supply, we employ the method of variations (tbe
marginal method) and thus obtain a picture of the whole process
in flux. A farmer has to choose between two ploughs, one of which
lasts ten years, and the other, equally useful, lasting eleven. If he
chooses the more durable (and dearer) plough, he has tbe benefit
of an extra year’s service, which, however, only comes into
being after the lapse of eleven years, and must therefore replace
the difference in price between the two ploughs accumulated
by the total mtexest for the eleven years. Similarly, the price
of old wine must exceed the price of newly-pressed wine by the
interest for the years of storage.

Professor Ca^sel holds that the real practical reason justifying
this distinction is that “ incomparably the largest quantity of
capital-disposal is required for the services yielded by durable
goods ” (such as houses, railways, etc.). Translated into everyday
speech this means that the greater part of annual savings,
together with the annually disinvested portions of capital, are
invested in this way. And this is what undoubtedly happens in
present-day society, but only because of its outstandingly
progressive character. In a stationary state, the situation would
be entirely different. The whole of this analysis furnishes but

CASSELLS SYSTEM OF ECONOMICS 241

one example ont of many of Professor CasseFs irrational
inclination to regard as normal wtat is from a quantitative
point of view a violently progressive society.

We come now to an undoubtedly valuable contribution to
the practical problem of interest. We are, or course, referring
to his celebrated calculations on the strong impulse to individual
capital-consumption and to a reduced total of capital accumula-
tion which a very low rate of interest would induce. (It is on
account of this tendency that such a low rate cannot exist.)
This element deserves all attention, but one cannot with
certainty infer any other conclusion than that saving and capital
accumulation will progress at a slower tempo the more the rate
of interest falls. And this seems to be clear a priori. Assuming
a sufficiently clear insight into the urgency of future wants as
compared with present wants, and also a sufficiently vivid
interest in the welfare of future generations, it will appear that
capital accumulation cannot cease, as long as it is generally
possible to gain more in the future by sacrificing less (computed
in terms of subjective values) in the present, i.e. as long as
there is a positive rate of interest, however small. In a socialist
state, the conception of which presupposes the fulfilment of both
these conditions, the rate of interest would therefore tend to
fall to a minimum, until it finally became zero. CasseFs
own views on “ interest in the socialist state ’’ are rather
obscure, and appear to be a survival of his bizarre ideas in
Das jBedfe”.

The important practical question of the structure of the
rate of interest in the immediate future, that is to say, until
the losses in capital incurred in the war are more or less made
good, depends above all on what happens to the population.
This book contains no chapter on the theory of population —
only a couple of pages m the chapter on wages are devoted to it,
out of sheer necessity — ^and the author’s own views on the
subject seem to be hopelessly vague. It appears as if his whole
system of economics is so mextricably bound up with the idea
of a continually and rapidly increasing population that he
cannot depart &om it, even when it is all too patently opposed
to the facts. Before the war, Bortkiewicz had already predicted
that the population of Germany would have become stationary
within perhaps twenty-five years. Since the war the probability

242 LECTURES ON POLITICAL ECONOMY

has become much greater, and the prediction need not be confined
to Germany alone !

Professor Cassel maintains that, even in a stationary state,
every fall in the rate of interest would produce an enormous
rise in the demand for fixed capital, e.g. for houses for labourers.
But this is by no means certain. The price of a house is not
made up of interest only, and, besides, the habitation of a large
house involves other outlays. Of these fuel was quite as expensive
in Sweden as the rent of the house itself — ^at least during the
war. The situation is entirely different when there is a great rise
in the standard of living of the labouring population, for then
it becomes certain, as the example of America shows, that the
workers’ demands for dwelling space will increase even without
any fail in the rate of interest.

All in all I fear that Professor Cassel has not succeeded in
throwing light on the problem of the probable future rise or fall in
the rate of interest, whether in its theoretical or practical aspects.

We must add that this chapter undoubtedly contains many
sound observations, e.g. on the question of the tendency towards
the concentration of firms (increasing returns proper) — a subject
which has hitherto been very much neglected by theorists. But
queer and arbitrary statements, whose only motive apparently
is a desire to controvert accepted principles, are to be found
in plenty, e.g, on pp. 227 and 228 among others. For reasons
of space, I must forego any closer examination of them.

No less than thirty-eight pages are devoted to the theory
of rent. We may well doubt the need for so exhaustive
a treatment, for nothing new is added to a subject which has
been discussed almost ad mtuseam and which is yet so simple
in essence. The pertinent criticisms of the Ricardian theory
had already been made by Walras and should by now be
considered common property in economics, even though no less
an economist than Marshall attempts to maintain Ricardo’s
teachings in their old formulation. It is in any case an abuse
of words to dismiss, as Professor Cassel does, Ricardo’s famous
thesis that ‘ the price of corn is not high because rent must
be paid but that rent must be paid because the price of com
is high as merely ^ false Rightly interpreted, it contains
an extremely important and often misunderstood tmth, and it
should not give rise to any real misconception.

CASSEFS SYSTEM OF ECONOMICS 243

Naturally, in actual fact, as Professor Cassel (following
Walras) rightly maintains, the price of land and its services
is determi n ed in more or less the same way as the prices of
other factors of production, and is only a link in the whole chain
of price-relationships. But if one tries to deal with the whole
problem in all its ramifications at once, it becomes so much
more complex and so much less susceptible to a general survey
that the whole exposition peters out in vague generalization.
If we are to obtain some real insight into the interrelations
of the phenomena, it is therefore necessary ^ to start with a first
approximation or abstraction, in which the quantities of goods
on the market are taken as given, and then go on to a second,
in which the prices of the goods are taken as given. This procedure
is equivalent to treating the problem of production (and
distribution) on the assumption that only one commodity is
produced — and yet even in this case it is complicated enough !

As an example of the looseness of analysis in this book,
we may cite the statement (p. 286) that in comparing two
pieces of land of different quality, we must not, as Eicardo
does, assume them to be worked by the same amount of labour
and capital ”, but by the amount of labour and capital adapted
to each. What is he driving at.? Eicardo himself says that the
better land is cultivated more intensively, whether alternatively
to or simultaneously with the cultivation of the worse, but that
does not imply that there is a lacuna in his deduction of
differential rent.

Professor Cassehs peculiar and mutually inconsistent
definitions of ‘‘ increasing and decreasing returns ” have already
been discussed.^ On p. 279 he adds yet a third, when he says
that if with a given price for labour, land, and capital an
entrepreneur can increase the value of his product relatively
to total costs by applying more labour and capital to a given
piece of land, a firm is still in conditions of mcreasing returns
But on the same assumption the entrepreneur could have obtained
the same addition to his relative profits by diminishing the

^ It was this method that I for my part adopted.

2 As in agriculture, we can usually manage without the terms increasing
and (after a certain point) diminishing returns. For as soon as the population
has increased to such an extent that the free products of nature (wild gra^
timber, etc.) have an exchange value, diminishing returns have already set in
and cannot be counteracted (but rather can only be shifted to a higher plane
by technical progress) — ^which Cassel himself seems to admit.

244 LECTURES ON POLITICAL ECONOMY

amount of land employed and thus reducing total costs. On tHs
excellent definition increasing ’’ and decreasing returns are
therefore identical !

The whole analysis is here very nebulous and diffuse.
Naturally, the entrepreneur strives to attain the maximum
absolute and not relative profit ; we must therefore necessarily
start from something fixed and given, or else the whole edifice
will vanish into thin air. We must assume that the entrepreneur
disposes over either a given amount of capital (his own or
borrowed), or else a given area of land, or finally a given amount
of labour (as in co-operative agriculture). But in this case the
Principie of Substitution only comes into operation for the
factors of production demanded by him and not for those he
already possesses.^ Only in a general equilibrium resulting from
competition between entrepreneurs, where their profits are
theoretically forced down to :sero, does the Principle of
Substitution or marginal principle hold universally. And yet
we must always introduce a reservation for ^"the marginal
productivity of capital"’ regarded as a sum of value. This
I have explicitly proved in my writings, but Professor Cassel
completely neglects it. His own rather vague and diffuse theory
of capital is wholly unadapted to more clear-cut conceptual
distinctions.

Greater store must be set on his really exhaustive treatment
of the rent of mines — ‘‘ the price of natural materials And yet
in my opinion his discussion would have gained in significance
if he had first dealt with what is theoretically the simplest case,
that in which the mines are regarded as inexhaustible, and at
the same time the annual output can be increased within certain
limits without increased general costs. This is clearly the
assumption from which Ricardo starts in his only too sparse
reflections on the subject. If in these conditions all mines should
be regarded as equally productive, there would, says Ricardo,
be no rent for the mine, and the price of the minerals would
include only labour and capital costs. When, on the other hand,
some mines are more productive than others, the owners of the

^ This limitation is also to some extent applicable to my analysis in
Lectures on FolUical Economy (p. 131 above), where I was dealing with increasing
returns proper. It was therefore possible to conceive of (e.g.) a trust with a
large capital consisting of many individual firms and striving after an optimum
size for each ; in this way it obtains a maximum profit on all its individual
investments of capital and on its capital as a whole.

CASSEL’S SYSTEM OF ECOXOIHCS

245

better m i n es enjoy a rent, wMcn is determined in tiie same way
as tbe ordinary rent of land.

Bnt tere Kicardo must be wrong. If on tins assumption
the better mines were released for free exploitation, labour and
capital would flow from the worse to the better mines, the
annual output would rise and the price of ore fail. We maintain
on the contrary that there would be no such change in the
price of agricultural products when the rent of land is confiscated
or remitted by the State. The owners of the better mines can
therefore only procure incomes by an artificial lowering of the
gross product, and even in this case there would be an essential
difference between ‘‘royalty’^ and ^‘renf. The former is
a monopoly rent, the latter a pure scarcity rent. When we
take an imminent exhaustion of the mines into account, the
difference is naturally accentuated, but it tends to disappear
to the extent that relatively increased costs are involved by
increasing the annual product of either mines or agriculture
in general. In any case, it is to Professor CasseFs credit that
he has gone into the details of a subject which has been only
too cursorily dealt with in economic theory.

We now come to the special chapter on wages. Here also
Professor Cassel claims to have constructed an independent
theory, hut I cannot discover wherein its originality lies. The
division of wage-theories into ‘‘ pessimistic ’’ and optimistic
is certainly not new. All wage-theories without exception — or
with the exception of those which are merely confused — ^are
necessarily pessimistic, if we start from an unrestricted tendency
for the population to increase, otherwise no wage-theory would
be pessimistic if pursued to a logical conclusion. Even the
Iron Law of Wages is converted into '‘a standard of life’’
theory or a Golden Law of Wages ” [Gide] — a change which
was by no means alien to Eicardo’s train of thought.

ll^y the Wage-Fund theory should be singled out from all
others for description as pessimistic is difficult to understand.
If we assume the ‘‘ dividend ” or fund to be sufficiently large
and the divisor (the number of workers) sufficiently small, the
quotient — ^the jper capita wages — can, at least at first glance, attain
any magnitude whatsoever. I willingly concede that the Wage-
Fund theory, in its classical form, where the fund was mainly
regarded as of a single year’s duration, was completely erroneous.

246 LECTUEES ON POLITICAL ECONOMY

As we have already remarked, it led even Ricardo to draw patently
false conclusions, and in this form it unfortunately became
a weapon in the struggle against the shorter working day.
In the extended form it assumed at the hands of Bohm-Bawerk,
it; can easily be defended from a purely theoretical point of view,
but it has, as we have said, a severe disadvantage from a practical
point of view. Eminently durable capital-goods cannot be fitted
into such a fund without involving the consideration of
altogether unmanageable periods of time. For shorter periods,
however, these durable capital-goods take on the same economic
status as land ; they are Rentengiiter ”, and their share (or
their owners’ share) in the product is determined, at least in the
stationary state, quite simply according to the principle of
marginal utility or of marginal productivity. A fusion of the
Wage-Fund and the marginal productivity theories, however,
would then be impossible. Or else one can ^ throw overboard
the whole concept of the Wage-Fund, or the subsistence-fund,
and adopt instead Bohm-Bawerk’s brilliant suggestion. The
idea of considering capitalistic production as primary and capital
itself as secondary was put forward in the second book of the
Positive Theory, but of course Bohm-Bawerk himself did not
carry it to completion. By this means everything is dominated
by the marginal principle applied to land, labour, and time (the
period of waiting or capital-investment) as the factors of
production.

Remarkably enough, in this chapter, Professor Cassel also
rejects marginal productivity as a ground for the determination
of wages ; he asserts inter alia that it provides no elucidation
of the dependence of wages on the workers’ efforts and ability ”.
This we fail to understand. In the individual case wages are
of course proportional to the worker’s eiBSiciency — ^in all cases in
the bargaining system. If the efficiency of labour increases all
along the line this theory drives us to the conclusion that wages
fall relatively (or possibly absolutely), but this sad result cannot
be ascribed to the fault of the theory ! Cassel adds that he is
afraid that efficiency and marginal productivity will be confused,
and in support of this view he quotes a passage from Professor
Seligman which is not very remarkable in its penetration, and
however prominent a thinker Professor Seligman may in many

^ For my own part, I have already made the attempt.

247

CASSEL’S SYSTEM OF ECONOMICS

respects be, we cannot bold Mm to be a typical representative
of modem economics in any way.

Wbat then are Professor CassePs own views on the theory
of wages ? It is not so easy to say. He begins by going back
to the principle of supply and demand, wHch always provides
a starting-point at any rate, if nothing else. But in its
elaboration he expresses himself, contrary to Ms wont, in quite
loose phraseology, as though he were afraid of certain unavoid-
able conclusions. The policy of “ the open shop ’’ described by.
the Webbs he praises discreetly, without, however, completely
binding Mmself to it. "'The Webbs’ doctrine has the great
merit that it has changed the study of the supply of labour from
a pure computation in terms of arithmetical magnitudes to an
examination of the underlying economic and social processes
which determine the supply of labour” — ^which sounds very
much like a verbal flourish. And as verbal flourish number two
I shall cite the following (p. 333) : “ The most advantageous
position for labour on the whole is attained if the supply of labour
is as nearly as possible adapted to the demand, i.e. if the price
of different kinds of labour is merely the expression of their
inevitable natural scarcity.” Can this theory be applied without
closer examination to those earning the lowest wages ? More
than once Cassel talks of the necessity of an ‘‘ amelioration ”
of these unfortunate wage conditions or of the market ”, and
still more often he warns us against any “ misdirected ” attempt
at such an amelioration, but he never teUs us how the desired
amelioration should be introduced.^

^ Undoubtedly, tbe cardinal mistake in bis approach is that be here, as
in his treatment of parasitic occupations and the like, always proceeds from
the hidden assumption that wages as such must necessarily be sufficient to
cover the labourers’ subsistence. Nmther theoretically nor often practically
is this hypothesis justifiable. Since the theories of a science must be generally
valid, it is perhaps permissible to conceive of a “ strong ” case. We shall
assume that in equihbnum, wages for most workers are considerably below
the subsistence-level, but that, at the same time, the total product is so great
that, with a different distnbution, it would abundantly cover the needs of aU.
From Professor Cassel’s point of view the question of an amelioration of the
conditions of labour in this case constitutes, as far as I can see, an absolutely
insoluble problem. For wages as such cannot be raised, at least not safely, unless
the population diminishes to such an extent that the marginal productivity
of labour is considerably raised. But such a diminution is a slow and, in mo^
cas^, painful process, and, moreover, in this particular case it would, on our
assumption, be completely unnecessary and therefore to be repudiated. The
only way out is to grant subsidies, of the consequences of which Oassel is so
fearful. If necessary, they must of course take on such a form that they do
not imply any humiliation for anybody.

248 LECTURES ON POLITICAL ECONOMY

When he discusses (p. 334) the question ‘‘ of a limitation
of the total supply of labour ”, he expresses himself so vaguely
that we cannot tell whether he is considering a shortening of
hours or even — and this more or less follows from the context —
a reduction in the number of workers, which naturally makes
an immense difference. On p. 349 he says that too small a relative
birth-rate in the higher classes and the upper sections of the
working-classes may “perhaps lead to a relatively too great
scarcity of qualified workers, especially in the key positions
This in its turn would involve a particularly disadvantageous
development of the market position for the lower classes, and
would press down their wages considerably. No doubt such
a chain of events is conceivable, but in any case it would be
hard to point out a historical example of this kind. A general
fall in the birth-rate is a phenomenon confined to comparatively
modern times.

As an explanation of the high wages of North American
workers we are offered (p. 339) — ^as far as one can gather from
a phraseology which is repeatedly loose — ^the theory that the
European demand for agricultural products prevented their
internal price in America from falling as much as they would
otherwise have done. If that is his real opinion, it is wrong.
This demand — ^as he hi ms elf admits immediately afterwards —
was responsible for the emergence of rent and to this extent
for a fall in wages (in terms of com) in America. Whether this
disadvantage has been counterbalanced by the cheapness of
European industrial goods is more than doubtful.

The chapter closes with several reflections on “wages in
the socialist state ”, which, like his previous remarks on the
same subject, suffer from being excessively critical to the point
of ineffectualness. He asserts inter alia that much, perhaps most,
of the incomes of the “ leisured classes ” to-day would not^ after
redistribution, accrue to the benefit of consumption in the
socialist state, because “ probably ” it “ will have to be claimed
for the requisite accumulation of capital ”. Which presupposes
a large continuous increase in population inconceivable in the
long rtin, whether in the socialist state or in present-day society.

On the whole, in spite of much that is interesting in detail.
Professor Gassers inquiries into the theory of wages are too
much devoid of rigour and-nso to speak— backbone, to provide

CASSIL’S SYSTEM OF ECONOMICS

249

the basis for fruitful social iavestigatioiis, although^ appealing
to a well-known monograph, he very emphatically stat^ that
such has been the case.

Ill

The third book is devoted to the nature of money and to
some extent to actual monetary systems. Even here the author’s
theories are not too rigorous or consecutive. As far as one can
see he is stiU completely dependent on the Quantity Theory, as
in Section 43 on Free Standards ”, The only concession he
makes to the bullion ” theory is to be found in the statement
that the hope of a future conversion of paper money into bullion
can to some extent afiect its value. Indeed, this is not incom-
patible with the quantity theory ; some-bank notes are hoarded
for future conversion and, for the time being, take no part in
circulation. Besides there are cases on record where paper money
has attained a value even higher than that of the bullion it
originally represented.

But in the chapter on Bank Money ” we suddenly stumble
on the following passage, which might almost have been
culled from one of Jacob Riesser’s pre-War works. No one
should doubt, at this time of the day, that these works exercised
a baleful influence on Germany’s monetary system during the
War. I quote the passage in full : —

l^ere is moreover a possibility of a continuous multiplica-
tion of the means of payment only as long as confidence in the
bank’s capacity to cash its notes and deposit is tindisturbed. But
as we know from experience, this confidence cannot be maintained,
unless the bank keeps a reserve which is in a sufficient proportion
to the obligations daily falling due and particularly to its notes.
In this respect an international desire for an appropriate reserve
has arisen, a desire which has not fixed upon a constant numerical
proportion without seriously upsetting confidence at home and
abroad in the maintenance of the foreign exchange rate. We
therefore find that a minimum reserve which is never actually
used IS regularly kept against bank money (!). This m i ni mum
reserve will be left untouched even in cases of the direst necessity,
as in wartime. What is more, it is just in such cases, as the most
recent experience has shown, that an earnest attempt is made to

250

LECTURES OJT POLITICAL ECONOMY

protect the reserve and even to strengthen it by diverse means by
abolishing the obligation to redeem the notes in cash/’ ^

Well might we ask — what is Professor CasseVs true opinion ?
Is it the scarcity of bank money ”, ultimately ensuing from the
interest pohcy of the banks, which determines the value of
money ? Or is it confidence in the conversion of bank-notes
and deposits in gold — confidence so touchy that it must always,
so to speak, have iis object, gold, visible before it, but at the
same time so impregnable that it cannot be perturbed when it
is patently deceived by the banks’ indefinite postponement of
conversion ? Of course one can only accept one of these views
to the exclusion of the other. There is no doubt, at any rate
for me, as to which has most to be said for it. In the nature of
the case, Professor Cassel should tend to hold the former — ^the
experience of the War, as he himself admits, must influence
him in this direction.^

When he is unravelling the influence of the rate of interest
on commodity prices, we meet the same regrettable half-hearted-
ness and uncertainty. Judging by many of his statements, he
is clearly aware that the essential factor must be the relative
height of the rate of interest in relation to the return the borrower
expects to get irom the loan, i.e. to the real rate of interest.
None the less he says ^ that a real rate of interest in
any other sense than the market rate does not exist ”, Very
strange ! The rate of interest on the so-called open market,
i.e. the discount for first-class jpa^er, which in fact constitutes
a kind of intermediary between prime bills of exchange and
mere cash, stands indeed in a looser relation to the average
yield on capital than does the bank-rate. Again, as far as this
yield, i.e. the real rate of interest, is concerned, it is actually

1 [This passage, which occurs on p. 366 of the first German edition, has
been substantially modified in the second English edition.]

* It is a matter for separate consideration that, at the critical
mon^nt he goes bwk on convictions, at least apparently ; for instance, at
^ spring (1919) he unexpectedly supported the lowering

of ™ bank-rate. Since then, judging by newspaper articles, he has

again held that the bank rate (though only the loan rate) should be kept up.

^ j first German edition, p. 382 ; first English edition, p. 418. In
the second English edition (p. 439) the passage has been modified and reads

as iollows: ** ‘a real rate’, in a sense other than that of the market

rate is a very unreliable mdicator for the banks’ mterest pohoy, since the
S^st rai^’^f^^ shown, directly and powerfully influenced by the banks’

CASSEFS SYSTEM OF ECON’OMCS 251

not observed, on the Stoci Exchange apart, perhaps, from its
indirect effect on the price of shares. Of course it cannot be
strictly determined numerically, but it does not on that account
cease to exist and exert its full influence on economic phenomena.
Heat would still exist even if there were no thermometers, and
so would electric currents even if we did not know how to
measure them by means of a galvanometer.

My own statement that a persistent, abnormally high or
low money rate must be cumulative in its effects on the level of
commodity prices Gassel calls ‘^a paradox which is obviously
only possible if we overlook the reactions on the capital market
of an unjustifiable lowering of the rate of interest

But how can the fact that a cause operates in the same
direction as long as it persists be called a paradox ? Clearly
my theory coincides with Ricardo’s theory of the effects of
a continued flow of gold into the banks. On the other hand,
it must be admitted that some forces come into play as a reaction.
Professor Cassel’s own discussion of these forces (on the preceding
page) does not appear to be particularly lucid. There is no
doubt that when a sudden violent rise in prices has set in, people
with fixed incomes or with incomes which have not increased
sufiGiciently are compelled to curtail consumption. This process
is equivalent to a real accumulation of capital, and to that
extent should lower the real rate. In normal conditions, however,
such a reaction should only be of secondary importance. Other-
wise, as Ricardo says, the banks are “ potent engines indeed ”,
they will be able to determine arbitrarily the height of the rate
of interest without any risk other than that attaching to a single
rise or fall in the level of commodity prices. Professor Gassel
was formerly wont to be the first to maintain that the banks
do not have this power.

What appears to me to be a still more serious defect is
Professor Cassel’s tendency to expound the theory of money
in such a way as to make it serviceable for some of the practical
ends in which he is interested. He holds inter alia that the
present high maigin of profits of private banks is especially
beneficial and must be left tmdisturbed. He therefore attempts
to render credible the theory that the rate of interest does not
normally have any effects worthy of mention on the volume of
^ [See first English edition, p. 479, n.]

252 LECTURES ON POLITICAL ECONOMY

saving. Naturally, lie cannot substantiate this view. Accordingly,
be erplains in tbe Introduction to bis chapter on Bank Money
(p. 412) that ‘‘in an inquiry into tbe nature of money, it is
clear that we must abstract from all deposits representing
investments of capital, and confine ourselves only to cash
entrusted to tbe bank on current account It is no accident
that this is a preliminary to bis tborougb-going refusal to attach
any importance to tbe deposit-rate in tbe determination of tbe
value of money. In tbe important Section 47 on tbe “ Cover
on Bank Money and its Reflux ”, Cassel assumes for tbe sake
of simplicity that “ tbe capital left in tbe bank for longer periods
or permanently remains constant and this provisional
assumption is never later discussed. And yet be himself must
recognize (p. 438) that a rise in tbe discount-rate will only have
a sufficiently powerful effect on tbe “provision of money”,
if “ the sum of money lent is large in relation to tbe bank money ”
(bank-notes or current accounts), in other words that tbe money
consisting of interest-bearing deposits (just as much as tbe
banks’ own capital) constitutes a significantly large part of
total liabilities. Tbe importance of deposit rates for a rapid
regulation of tbe issue of bank-notes (or bank money in general)
clearly follows ; at tbe same time it is tbe basis of tbe modern
demand that tbe central banks should also be allowed to receive
deposits in return for tbe payment of interest — as the Bank of
England actually did during the War, at least for the private
banks.

Although be elsewhere keeps only to tbe closed economy “ on
principle ” (!) Professor Cassel also deals here with international
payments and tbe foreign exchanges. Characteristically enough,
be begins with “ free independent standards ”. This is indeed
a very difficult and complicated question ; in any case bis theories
do not seem to me to be well developed. He asserts that a high
exchange rate in one country — e.g. Glermany — ^acts as a stimulus
to borrowing from abroad on short term and to the export of
securities, because in both cases “ there is a profit to be earned
on tbe high exchange ” (p. 512). That may well be, but is this
result certain ? Tbe man who procures a deposit abroad will
one day have to pay for tbe loan. If tbe exchanges continue at
tbe same rate, be has gained nothing, and has offiiy bad to pay
^ The italics are mine.

CASSEL’S SYSTEM OF ECOXOiflCS

253

what was probably an exorbitant rate of interest in the interim.
Similarly, the price of foreign — e.g. Swedish — securities must rise
in Germany, while German securities fall in Sweden if the mark
depreciates relatively to the krone ; how then can it pay to
export them from Germany to Sweden ?

The explanation must be as follows. The man who buys
securities in Germany in order to sell them in Sweden is not —
as Cassel says — a speculator in the proper sense of the word,
but is merely conducting an arbitrage operation, the gain from
which, if any, he can calculate directly. Actual speculators are
the final buyers or sellers of these securities. The German owner
of Swedish securities sells in the hope that he will be able to
repurchase at a profit when the mark exchange rises again.
He can therefore sell them at a somewhat lower price than that
corresponding to the rise in the exchange-rate, or otherwise
it would not pay him to do so. On the same grounds a Swedish
buyer expecting a future rise in the exchange on Germany offers
a little more for German securities than would correspond to the
present rate of exchange, and so on. The same holds for Swedish
imports from Germany. If the payment is stipulated in Swedish
money and the exchange-rate on Sweden rises, the German
buyer obtains a postponement of his payment, if necessary,
against the payment of a higher rate of interest, because he
hopes for a future fall in the exchange-rate. If the payment
is made in German currency, the Swedish creditor, for this
reason and no other, allows his claim on Germany to remain
outstandmg instead of pocketing it at the current low rate of
exchange on Germany.

One of two conditions is necessary, if a country having
no interest-claims abroad is to be able to import more than it
exports. Either a country offers its creditors an attractively
high rate of interest by raising its discount rate, or its foreign
exchange-mte has fallen sufficiently to attract speculation on its
prospective xise.^

Of course the level of commodity prices and the exchange-
rate always tend to move in the same direction in two countries
trading with each other, at least as long as the exchange of
goods can proceed freely, but this movement may just as well

^ Cf. my article in EhmomisJc Tidskrift on “ The Riddle of the Exchanges”.
To judge by an article in Sv, Export, No. 17, 1913, Cassel seems to have now
accepted this view.

254 LECTUEES ON POLITICAL ECONOMY

start from the side of the exchange-rate as from that of the
price level. With a higher exchange-rate there is a rise in the
price of exports as well as of imports, and if the banks do not
appropriately react with a higher discount-rate, but let their
bank-notes and credit flow out, the rise in prices is rapidly
diffused to all commodities. Thus the credit policy of the banks —
and above all of the central banks — ^is the dominating factor.

With some astonishment we find Professor Cassel repeating
in this book without any further critical examination his
celebrated speculations — ^more fantastic than trustworthy — on
the relation between the quantity of gold and the level of
commodity prices throughout the nineteenth century. No one
denies that some such connection must exist, but in order that
it should be demonstrable in detail, all the factors at work must
naturally be considered, and this he has completely neglected
to do. We have heard tell of an American humorist who once,
probably in the great days of the Temperance movement, gave
an evening lecture with the queer title of “ Milk which began
with a promise not to mention the word milk again. He succeeded
without any difficulty. Professor Cassel has solved the much
more difficult problem of giving us a numerical analysis of the
connection between gold-production and the price-level from
1800 onwards without as much as mentioning silver on a single
occasion. I am by no means the first to draw attention to this
omission, it has been done several times before now — ^in Sweden
more than ten years ago by Brock. But it is still entirely ignored ;
he continues to ‘‘ conjure ’’ with his gold-curves. Of what use
are such ingenious constructions ? The more they succeed, the
more suspicious become the very methods which, when rightly
used, should inevitably lead to a demonstration of the gap in the
argument, at least for what covers the nineteenth century, when
the world’s main metallic currency was silver. If he had extended
his curve to cover the eighteenth century, then, as far as I can
see, their disagreement with the facts— -not to say their absurdity
— ^would have immediately become apparent.

IV

My review has become exceptionally long, or otherwise
I should willingly write at rather greater length on the fourth

255

CASSSL’S SYSTEM OF ECONOMICS

book on Trade Cycles in order to compensate for my previously
largely negative criticism. As I have already said, it is in my
opinion incomparably tbe best part of bis work. Professor CasseFs
great gifts for concrete description based on facts and figures
here show to advantage. Besides, tbe somewhat irritating
Olympian omniscience of tbe rest of tbe book bas entirely
disappeared ; be never claims to bave propounded some new
theory of crises, but is content to sujfier tbe older explanations
of crises calmly and objectively and to accept tbe most plausible
of them. At tbe same time be illuminates all tbe phenomena
associated with tbe trade cycle with interesting statistical
tables and diagrams.

Considering tbe extraordinary difficulty of tbe subject (and
my own far from adequate comprehension of it), I certainly
cannot vouch for tbe correctness of all bis conclusions, but
on tbe whole they appear preponderatmgly sound and just.

Some objections can certainly be advanced ; tbe description
of tbe period of depression, which is tbe weak point of most
theories, hardly emerges in a clearer light in Cassel. From bis
older essay (Ekonomisk Tidskrift, 1904), on which this is otherwise
a great advance, be bas taken tbe idea that capital accumulation
even in a depression mainly takes tbe form of fixed capital. He
tries to show by means of tbe statistics of railroad construction
{inter alia) that the increase in fixed capitabgoods does not
stagnate even in tbe downward phase of the trade cycle ; so
that society is better provided with fixed capital at tbe end of the
depression than at tbe beginning. He forgets that all this must
be judged relatively. Tbe provision of fixed capital must always
keep pace with tbe growing needs of the population. If its growth
is actually accelerated in tbe boom and retarded in a depression,
tbe latter from this point of view cannot serve as “ a preliminary
to tbe subsequent upward phase ’’ — other than negatively by
creating a relative vacuum which must be filled. Logically
speaking, what Professor Cassel says must bold for circulating
capital — stocks of goods. What in fact happens cannot,
unfortunately, be ascertained owing to tbe lack of statistical
material. Professor Cassel does not wholly deny this possibility,
but be is generally tempted to keep it in the background.

Tbe agricultural situation is particularly relevant at this
point. If, as be also maintains, agriculture relinquishes some

266 LECTUEES ON POLITICAL ECONOMY

labour to industry during a boom, it must on tbe other hand
be possible to do some preparatory '-work in the subsequent
depression, which will serve to provide food for the population
in the next industrial boom. For during the depression a number
of industrial labourers return to agriculture, which can also
absorb part of the increase in the labouring population. Professor
Cassel thinks — ^in my opinion wrongly — ^that agriculture is
independent of trade cycles proper, thus differing from Dietzel
and Petander, who perhaps go to the other extreme.

Here and there we still find inconsistent and loosely
reasoned judgments. On p. 609 it is left an open question how
far real wages (as distinct from money wages) rise or fall in
a boom. But only a few pages later, without giving any really
decisive reason, he is sure that they rise, at least if the services
of those recently taken into employment are considered. Brock
has maintained the opposite thesis, and the statistics he adduces
would have deserved some scrutiny. The scepticism with which
Professor Cassel here speaks of statistics ’’ does not well accord
with his own diligent application of statistics as a method of proof.

All these are mere details. One reads this painstaking
discussion with interest and advantage. And what is more
with enjoyment. The very tone is different. Curiously and
characteristically enough it is just at this point, where he has
really so much that is new and valuable to offer, that an
unassertive, quiet and scientific approach redeems the unpleasant
aggressiveness of the preceding part of his work.

With a certain feeling of constraint we ask : why could it ’
not all have been written in tins spirit ? Why has not Professor
Cassel throughout contented himself with the role of continuer
instead of that of a pretended innovator, for which neither his
nor other men’s powers suffice when it is a matter of so large
a field as the whole of economics ? Why has he not resolutely
freed hi ms elf from the immature vagaries of his earlier writings
— ^which he cannot seriously maintain — ^and, with the acuter
view which he must have acquired, given us a simple objective
survey of the present position of economic science ? That the
work even in its present form has many merits, I do not deny ;
but — ^and this is the highest compliment I can pay to his talent
— ^he could have enormously improved his book if he had cared
more for the subject than for his own self-esteem.

CASSEL’S SYSTEM OF ECONOMICS 257

Macaulay mentions as a characteristic of James II that
when a member of his court dared to contradict him and humbly
warn h i m against the conse<juences of his explicit avowals, he
used to repeat what he had said in identically the same way
and then believed that he had mfficiently refuted all objections.
Such a method may be all very well for kings in difficulties,
although, as the example shows, it has its dangers even for them.
For laymen who have not yet become the acknowledged monarchs
of their subject it is decidedly not to be recommended. Professor
Cassel must learn — ^unless it is indeed too late — ^to use his critical
faculties on hi m self as well as on others, to give as yrell as to take
— otherwise his life-work will not survive criticism.

2. Real Capital Am> Intekest^

(a) Dr. Gnstaf Akennan’s Reallcapital und Kapitalzins

It has been a great pleasure for me to re-read in print
a book in which I had already taken a keen interest in its
manuscript form, especially as what remained rather obscure
in the perusal of the manuscript now stands in a clearer light.
This holds for the defects of the book as well as for its merits,
but on the whole I believe that it is with a good conscience that
I can give the author credit for having fulfilled his anything
but easy task with rare energy, consistency, and deep
penetration. The object of the book is to investigate the
co-operation of social durable capital with free uninvested labour
in production. This problem is clearly of great practical
significance — ^no doubt much more so than the problems dealt
with by Jevons and Bohm-Bawerk. They concentrated on the
capitalistic process of production, in which labour resources
(and probably land resources) ripened into immediate consump-
tion goods, or what the author calls variable capital But his
problem is so complex that the vast majority of economists,
including the reviewer, have almost entirely passed it by as
being much too difficult to be susceptible to analysis. In spite of
the fact that Walras did touch on certain aspects of the question,
our author has not much to draw from him, for Walras essentially
regards capital-goods as indestncctible or as constituted in such
a way that they can be kept intact with a given amount of
maintenance (or insurance) costs. This procedure naturally
simplifies the problem, but on the other hand it neglects many
of its most important aspects. For Walras does not take into
account the fact that a longer or shorter duration for the
projected capital-good may be more profitable, which is the
crux of the matter for Akerman. But as the author himself
admits, the real starting-point, if nothing else, of his own

^ This article first appeared in the Ehonomxsk TvdskrtH, 1923, Nos. 5-6.
pp. 146-180. •' ^ '

258

EEAL CAPITAL AND INTEREST 259

treatment was discovered in the long-forgotten work of the
Scottish-American, John RaeJ

From the very beginning the author has therefore to go
almost entirely his own way. Oux esteem for his work rises
still more, when we remember that his problem is not elementary
from a mathematical point of view, and that in order to master
it he only had access to the ordinary high-school knowledge of
mathematics. Nevertheless, it is for this very reason that he
has been compelled to give his analysis such a form that the
book can be read by anybody without any but the most
elementary knowledge. But with one intractable condition —
the unremitting attention of the reader is demanded. If we
miss our way only once in the iSnely spun web of reasoning,
everything we read later is bound to be in vain, and it only
remains for us to begin again de now. Which is naturally
a shortcoming. The author ought to have relieved the reader^s
tension with a fuUer and more pointed method of exposition,
and would have been in a position to do so if he had more time
at his disposal. We may mention as an example of the
difficulties confronting the reader the magnitude representing
the value of a unit-use of some capital-good, e.g. a machine.
This magnitude 6, together with I (wages) keeps on appearing
in the whole of the latter part of the book, and is obtained
in the following manner. W^e conceive of the productive services
of this machine in a unit of time, e.g. a year, as being divided
into as many equal parts as units of labour required to produce,
not this machine, but an equally good and useful one of a single
year’s duration. This concept is indeed extremely abstract in
character. Certainly it is developed with unfailing consistency

^ Statement of some New Principlea of Political Economy. Unfortunately,
I only know hjs work through Bohm-Bawerk’s quite detailed and largely
eulogistic description of it (in the Qeschichte und KrUik der Kapitalzinstheorie),
Bohm-Bawerk’s criticism is in efiect identical with his celebrated objection
against all “ productivity theorists ”, who in his opinion constantly confuse
physical and value productivity. As I have already attempted to show in
Uber Werty Kapital und Rente, at the very most this confusion is nothing more
than a methodological error. In the first approach to the solution of the
problem of production and distribution, it is permissible, if not advisable, to
consider the prices of commodities as constant (which in the last analysis is
essentially what Bohm-Bawerk himself does) ; in the same way, we r^ard
production as constant in the first stage of the solution of the problem of pricing.
It is only at a later stage that we should combine both these approximations
in order to obtain the final solution of the problem. Once this is grasped, then,
as far as I can see, Bohm-Bawerk^s objection loses its force.

260

LECTURES ON POLITICAL ECONOMY

and does lead to correct results, but only by inflicting on the
poor reader tbe torment of keeping this whicb is neither

fish nor fowl, in mind. With a slight revision of the formula
the book could have been made more intelligible in this respect.

But there is another more serious difficulty, which I fear
is for the most part insuperable in the discussion of the economic
phenomenon of durable capital. For we cannot, at least without
further analysis, apply the celebrated principle that capital is
or corresponds to a certain amount of ' previously-done ’ labour ’ ’ ,
i.e. the accumulated saved-up, or invested, resources of labour
{or land). A machine fresh from the factory undoubtedly
represents a certain amount of labour ; if this were the machine’s
only cost of production, and if the usefulness of the machine
is taken as known, we can theoretically calculate at what rate
of interest these costs will yield interest for the lifetime of the
machine at the same time as they are being repaid. But if the
machine has been in use for over a year or for several years,
there remains only one part of the “ annual use ”, which, for
the sake of simplicity, is assumed by the author to be constant
in size or technical value. Clearly it is then quite impossible to
decide how much of the previously invested labour resources
still remain ‘‘ stored-up ” in the capital-good. In fact the
question has no meaning to which any proper sense can be
attached. For the annual uses successively following one another
constitute a kind of joint-supply (to adopt Marshall’s terminology)
and fundamentally it is just as absurd to ask how much labour
is invested in either one or the other annual use as to try to find
out what part of a pasture goes into wool and what part into
mutton. It is only at the margin of production that these
quantities can be differentiated and have a concrete significance
assigned to them.

It so happens that from the very beginning the author
is convinced that the problem is capable of solution in one way
or another. The whole of his intricate terminology bears witness
to this conviction. In addition to the concepts of investment-
capital and “ real value capital ”, both of which have a perfectly
real meaning, Akerman employs those of amortization capital
(in German, Tilgungskajdtal) so-called, transitory capital,
maintenance capital, concrete real capital, etc. “ Investment-
capital,” i.e. the labour costs of manufacturing a machine

EEAL CAPITAL AND INTEREST 261

is first divided into parts— into the so-called i-series. Tlie first
term of tliis series corresponds to the amount of labour required
to make the machine last only a year, the next term is the
additional cost of making it last yet another year, and so on.
This idea borrowed from Rae, even if abstract, is quite scientific ;
but it only has practical significance at the margin of production
where it pays to exchange a machine lasting ten years for one
just as good in other respects but lasting an extra year. But,
in addition, the author believes that the capital bound up in
a machine is after a time disinvested or amortized (and in
a stationary state reinvested) in the following order. In the first
year we regard the machine as repaying part of the investment-
capital and the interest accumulated on that part for a sifigls
year. Next year it repays another, rather smaller, part of the
initial investment costs, but with a total accruing interest for
two years, and so on, until the machine becomes finally worthless,
but at the same time is finally amortized. These amortization-
quotas, or rather the amounts of labour they are taken to
represent, form the t^-series, which of course is quite different
from the i-series, although their sums are equal. (Similarly,
if we use the rate of interest for a moment of time in our
calculations, in equilibrium the last terms of both will be equal
at the margin of production.) But in the first part of the book
the i^-series is often inextricably associated with the terms of
the i-series in a most confusing manner. The author holds
that this ^^-series, also called the ‘‘ abstract amortization
system” has a really scientific significance, or is at least of
great interest for purposes of exposition. I shall not bother
to deny the latter, but essentially it is only one of an infinite
number of other conceivable amortization systems. Nor has it
the advantage of leaving the capital situation of the owner
of the machine intact, for if the amount amortized is reinvested
on the basis of another amortization system, his supply of capital
will clearly increase at the beginning only to diminish later.
Consequently, it is only at the end of the machine’s existence
that taken together they become equal to the amount of
investment-capital. (It is assumed that the interest received
is consumed.)

If the owner of the machine wishes to maintain his capital
intact, he has instead to choose either the “natural” or the

2G2 LECTURES ON POLITICAL ECONOMY

“ theoretical ” amortization system. As far as I can see these
two systems really coincide. They can best be described in the
following way. Each year we write off or reinvest the difference
between the outstanding value of the capital-good at one point
of time, and its value at the succeeding point, e.g. at the
beginning and end of each year ; this procedure may indeed be
called perfectly natural ”, but the concept does not therefore
obtain any “ concrete ” content — ^neither more nor less than that
of the theoretical ” system. (A fourth system, the so-called

practical ” system, in which each year we write off an equal
fraction of the original value of the capital is also applied now
and then, but only because of its simplicity. It has no other
raison d'etre.)

Now if production is staggered ” {durchgestaffelt — ^to use
Bdhm-Bawerk’s term), machines of all sorts of durations
manufactured in different years are employed side by side in
the same firm or group of firms, and the oldest machine (or
machines) is annually exchanged for a new one. In this case
it is a matter of indifference which amortization system we
choose, provided that we apply it consistently.^ For m all so
much is always written off from the estimated value of existing
machines as is required (under stationary conditions) to
repurchase the new machines and consequently to maintain all
the machinery at a constant magnitude and composition. On
the other hand it is not a matter of indifference for the booh
value of the existing capital, for if we write off more at the
beginning of each machine’s ‘'life-time ” and less later, the total
book value of all machines clearly becomes less than would
be the case if we chose the reverse method. Here also the
“ natural ” system is to be preferred.

The book value of all the existing machinery becomes
exactly such that the yearly interest in them, computed at the
same rate as that actually yielded by the amortized or newly
invested capital, corresponds to their total yield per annum.
In perfect equilibrium this rate ought to be identical with the
prevailing rate of interest. This principle is demonstrated by
the author (on p. 151), but at bottom it is a mere truism, for the
outstanding capital value of the machines which have been

^ eg. an amortization system for the t-series could here have been chosen,
whicn would naturally have been impossible in the case of a solitary machine.

EEAL CAPITAL AND INTEREST

263

partly used up lias in fact just been computed by applying tMs
very rate of interest.

It might appear strange that the same physical capital
can just as well be taken to have a greater as a smaller amount
of labour resources invested in it. But if we remember that
static ’ capital always has a dynamic pre-history, the paradox
is resolved. The more the owner reinvests, the less the capital
that has to be supplied from outside before the collection of
machines of different durations becomes complete, so that a
perfectly stationary state has been reached. The smaller the
portion of the present value of fixed capital he can, if he wants,
regard as invested wages— and in this sense as capital —
the greater the part he may regard as interest which has been
accumulated but not yet consumed. If the firm is sold, he will
receive this interest probably in the form of profits over and
above the book value of the stocks. (But naturally we ought
not to think that this form does in fact yield a rate of interest
corresponding to the relation of the net gain per RnTimn to the
book-value of the capital. When, after a time, the owner buys
new machines to replace those which have been worn out, and
thus reinvests some of the successively uninvested capital, in
equilibrium the reinvestments will only yield the current
interest.)

The author’s adherence to the idea of ‘‘ concrete ” capital,
consisting of invested labour, leads him to hasty conclusions
which I shall discuss later. In my opinion, he would have saved
himself much unnecessary trouble if the t^-series and the whole
discussion, however interesting in itself, of the different
amortization systems had been completely omitted. For they
have no special function to perform in the actual solution of the
main problem. Their irrelevance is due to the fact that the
annual costs of maintenance of real capital are always amortized
and reinvested in their totality, whichever the amortization
system adopted for particular capital-goods. This quantity is
obviously proportional to the amount of labour invested per
annum, and also determines the amount of free uninvested

We have how reached the stage where, with only a few
simplifying assumptions, we can ascertain and describe
numerically the connecfeicm..h2fc^^^ essential constituents

264 LECTUEES OK POLITICAL ECONOMY

of the economic phenomenon of durable capital, viz. the yearly
product, wages, and interest for each given amount of capital
per head of the labouring population. The author considers in
turn diSerent economic situations where capital receiving its
Tnf9.Y?TrinTn remuneration only suffices for an investment lasting
one year, two years, or three years, or for an investment lasting
for an intermediate period. (Clearly the different amortization
systems, and consequently the book-value of fixed capital, will
not play any decisive role if this method of approach is
employed.)

The author makes two basic assumptions about the forms
of the productivity functions. The first is concerned with the
i-series, i.e. the amount of labour which has to be invested in
order to produce a capital-good of a given size and utility and
make it last for one, two, or three years, and the second with
the form of the productivity function, given the (most
advantageous) co-operation of a certain amount of “free”
labour with a certain amount of capital. Both these functions
must be regarded as technically given. To the latter Akerman
gives a definite mathematical form, but the former, later called
f{n) is only empirically determined by the successive differences
in the i-series.

If the relation between I wages and b the value of the
unit-use of a machine is taken as given, it can be shown that
a particular “ life-time ” for each newly -manufactured machine
produces the maximum interest on the capital so invested. The
author solves this by no means elementary problem of
ma x i miz ation with elementary tools, and in a particularly
ingenious and lucid manner (pp. 110-14). From a purely
expository point of view this is one of the best passages in the
book. He then introduces a situation in which a number of
different machines co-exist, although they were all manufactured
in different years. We thus obtain a static state in which there
is a “staggered” and constant production of machines and
consumption-goods. For its actual renewal or “maintenance ”
this complete equipment of machinery demands the exact cost
incurred in makmg a single new machine. Thus to each labourer
who is continuously occupied in manufacturing machines, there
corresponds a definite amount of machines now being used (and
of course an equal amount of “ machine-uses ” available per

265

EEAL CAPITAL AND INTEREST

diem or per annum). Similarly we can calculate the present
discounted value of the outstanding uses of all the remaining
machines, and consequently their present capital-value
‘‘ Realwertkapital This we do simply by applying the most
advantageous life-time, which has already been provisionally
determined, and the yield of every machine which has
recently been manufactured. (Adoptmg a different amortization
system the author also works out the results for two other
concepts of capital. But I pass this section by.) Given the
most profitable life-time for machines, the number of labourers
employed m the production of machines and the value of the
machine-capital are mutually determined. As soon as we
know the former we also know the amount of free labour
resources, for these two are together equal to the whole of the
available supply of labour, or the annual labour resources of the
society.

Now the free labour resources are combined with the
unit-uses of the machines available in each year. At this point
the productivity function is assumed to be technically given.
In perfect competition it must be homogeneous and linear,
i.e. such that a uniform increase in all factors of production
produces the same percentage increase in the product, in other
words, such that, after a certain optimum size has been reached
for the individual firms, production on either a large or a small
scale is relatively just as profitable. This function gives the
hjq)othetical size of the national dividend per annum, and by
its partial derivation we obtain — ^also hypothetically — I the level
of wages and b the value of the unit-use of the machine.^

Now in equilibrium these quantities, I and 6, must clearly
coincide with their initial hypothetical values. In other words,
we have to determine six or seven unknowns, i.e. the duration
of the capital-good, the rate of interest, and the distribution of
the existing labour force between machine-labourers and free
labourers, in addition to the three quantities already mentioned.
In mathematical parlance, these six or seven unknowns are

^ This is the only point at which Akerman makes nse of higher
mathematics — ^following my “ Lectures ” more or less closely. It shoiUd
not, however, have given rise to some of the insuperable difficulties which
crop up in the treatment of this part of the problem ; even in its elementary
form it would have been better had he proceeded much as I did in my per-
functory attempt to solve the problem in the passage dealt with.

266

LECTURES OX POLITICAL ECONOMY

determined by the same number of simultaneous equations,
which are transcendental to boot. The author solves this
formidable problem empirically and approximately by the
construction of arithmetical tables of the same kind as those
used by Bohm-Bawerk, though they are naturally more
complicated and more awkward to handle.

The book’s most brilliant and most significant contribution
to economics is not only to have put this problem (which I have
merely outlined with the greatest brevity) in all its detail, but
also to have solved it empirically. It can be argued against
the author’s use of figures that it is often hazardous to decide
to what extent the results gained are of general validity or are
dependent on the actual selection of the arithmetical data.

An increase in capital must bring about an extension of
the life-time of a capital-good, so that capital grows not only
in “breadth” but also in “height”. Otherwise the marginal
productivity of labour would necessarily rise in comparison with
that of the use of a machme. This consideration, as I shall show
later, always makes it advantageous to increase the durability
of the machine, and this is further corroborated by the author’s
tables, though the result is somewhat obscured by his assumption
that the extension of the life-time of a machine occurs not
continuously but in one-year stages.

On the other hand, how far capital, when it grows, must
also grow in breadth remains less clear. The author’s Table III
(p. 144) shows that the amount of labour u — i, which is needed
for the maintenance (renewal) of durable capital, increases
continually, though not at a particularly violent rate, when
capital itself, and with it the life-time of capital-goods,
is increasing. We ask ourselves whether the solitary exception
here is perhaps merely apparent and whether therefore we are
even here dealing with a general rule. This appears to be the
author’s view on p. 28, where he says that when there is an
increase in capital “a greater amount of labour than before
must each year be employed in investments which partake of
the nature of the replacement of durable capital-goods, and
thus a smaller amount than before co-operates with the existing
capital-goods But this passage might only be a lapse, for
an increase in capital need not have the results here indicated
by Akerman. We can, as I shall show later, construct

REAL CAPITAL AKD INTEREST 267

a productivity function proper and a function for extending
tte life-time of durable capital-goods (tbe autbor’s/fn) or i-series)
sucb that, given no changes in population, both the labour
invested in machines and free labour remain constant when
capital increases. In this case capital grows exclusively in
height and not at all in breadth. With the appropriate
assumptions it is possible to make the former diminish — ^though
not of course — indefinitely — ^with a growth of capital.

But Table IV (p. 149) shows a continual rise in the mlue
of the annual product when capital increases and the rate of
interest is still positive. Is this rule general ? Clearly it is not.
For as long as the process of prolonging the life-time of the
machine always results in relatively smaller costs of maintenance,
it might appear to be in the interest of the capitalists to undertake
such a prolongation, even if the value of the gross product is
thereby diminished. If the capitalists combined, it would
certainly be possible for them to prolong the life-time of the
capital-good to their own advantage, even if it involved a fall
in the annual product, and would therefore be anti-social in its
nature.^ Can this also occur even in free competition ? No.

Actually it was this point which more than anything else
attracted my attention when reading the manuscript, and it is
of such intrinsic interest that Akerman might well have discussed
it in greater detail. In the manuscript version the author had
in place of Table IV a table from which it apparently followed
that the product per annum does not continually grow with
a rise in the amount of capital, but ultimately begins to fall,
even before the rate of interest has fallen to zero. Akerman and
I had a prolonged discussion on this point, and we finally arrived
at the conclusion that this result depended on the fact that the
productivity function, which after all was quite empirically
chosen by him, did not satisfy the preconditions for free com-
petition — ^in other words it was not homogeneous and linear. The
author later reconstructed this table and thus opened the way to
a consideration of the function P = AV c r mentioned on p. 137,
which is applicable to free competition.^ But it has the

1 We have a parallel case in investment in ** variable capital Cf. my

Uber Wert, etc., p. 104. , , - j *

2 Clearly, if the factors of production c and r are both mcreased in tne
same proportion, then, since k is & constant, the product P is also mcre^ed
in the same proportion. [P is the product, c is free labour, and r the machine-
capital with which it co-operates. Cf. Akerman, RealkapUal, p. 41.]

268 LECTURES ON POLITICAL ECONOMY

disadvantage of holding (in my opinion needlessly) only for
a special case, so that the figures for the product increase without
intermittence. As I shall show later, this result should also be
perfectly general.

Similarly, if we postulate the existence of free competition
and disregard the effects of inventions, wages should rise in all
cases with an increase in the amount of durable capital. But as
Table IV clearly shows, they will rise less than proportionately
to the increase in capital. In other words, although the extension
of the life-time of capital-goods cannot entirely frustrate a rise
in wages, it is adopted in reaction to such a rise, which has
already taken place.

I must adopt a more sceptical attitude to the statement on
p. 152 ff., even though it is made with certain qualifications.
On variable capital ” I have observed in my own writings
that von Thiinen’s thesis that the rate of interest is determined
by the addition to the product due to the “ last ’’ portion of
capital does not hold for an increase in the whole of the social
capital. It is only valid for a low rate of interest, since part of
the increase in capital is absorbed by increased wages (and rent)
so that only the residue of the increase in capital is really effective
as far as a rise in production is concerned. The author now says
that von Thiinen’s thesis may hold even for social capital if only
w^e take into account the increase in concrete’’ capital, i.e.
the amount of labour recently invested to the value of the
previous increase in capital. This should probably prove to be
right, if only we could always, so to speak, catch hold of this
concrete capital. For example, the principle holds perfectly
for Bohm-Bawerk’s schema (vide Appendix). But in the
arithmetical demonstration here given, it only depends on the
fact that capital-goods invariably last for a single year and
no more, so that capital grows exclusively m breadth, and thus
proportionately to the amount of labour annually invested.
Akerman further assumes that it takes a year to manufacture
any capital-good. To obtain a picture of the process as a whole,
we can imagine a supply of free labour always co-operating
with another supply of labour, which has already been invested
for exactly a year and is now maturing ”. The problem now
becomes extremely simple, and the result is really only an
application of the principle that “interest is the difference

REAL CAPITAL AND INTEREST 269

between the marginal productivity of saved-up (accumulated)
labour and^ that of current (free) labour ”, but it is actuaUy
much too simple to permit of drawing any conclusions for fixed
capital lasting for several years. For the inter-relations are
much more entangled here, and as we have said concrete capital
(so-called) has no proper significance in this case, ikerman
himself admits that his tables cannot provide any complete
corroboration of this defimtion of interest. Characteristically
enough, he does not seem to be certain which of the numerous
capital concepts he has defined should be used as the basis of
his calculations, but he beheves that better results will be
obtained by adopting the rate of interest at a moment of time
and by applying ‘‘ higher mathematics ” to the problem. As
I was rather interested in the subject, I undertook a minor
piece of research of this kind, which I append at the end of
my review. It leads to a particularly interesting result, but the
above definition is not corroborated.

Bohm-Bawerk (and in fact Jevons also) describes interest
as being determined by the relation of the last addition to the
product to the extension of the period of investment, or to put
it in another way — ^by the margiaal productivity of waiting
Much to his disappointment the author has not succeeded in
showing that this definition, closely related as it is to the one
just discussed, is compatible with the results of his tables ;
this is because he is dealing with a constant investment
period of a single year. This discrepancy depends on an omission
on the author’s part — an omission to which, I believe, attention
was already drawm at Akerman’s viva voce examination. With
his formulation of the problem, he should have taken not the
value of the annual product, but the (total) sum of wages paid
out in the course of the year as the divisor. (If simple interest
is applied, as in Akerman’s analysis, we ought generally to
calculate the interest accruing on the original capital and not
on the increasing products.) Once this factor is taken into
account, his tables are brought into agreement with Bohm-
Bawerk’s definition, though it does not follow that anything
is demonstrated for the general case. We are here confronted
with the thorny question of the average investment-period. In
this case it was due to the simple character of the problem that
the author could — ^apart from the above omission — deal with

270 LECTimiS ON POLITICAL ECONOMY

tHs concept, the average investment period is here only another
way of expressing the proportion between labour which is and
labour which is not invested* But not so for staggered
production. For instance, m the Bohm-Bawerkian scheme the
average period of investment for capital in the process of
maturing at each moment of time is half the period of production,
and this magnitude constantly appears and reappears in the
formulse. But it can easily be shown {vide Appendix) that the
average period of investment for all capital is a third of the
period of production; and I do not see how this magnitude
and its successive modifications could possibly be put in a simple
relationship with the variations in the net product. Perhaps
I have misunderstood the author or else am merely mistaken —
if so I earnestly hope that I shall be corrected. But it really
does appear to me that Akerman has here been involved in an
attempt to solve an insoluble problem. Clutching at any straw,
he says that if the two quantities are compared in a certain
position, they both become zero at the same tvme, which of course
does not prove that they are generally identical.

Actually the disagreement lies in the nature of the subject-
matter, and we cannot blame Akerman save for pronoimcing
a judgment he could not satisfactorily substantiate. At the end
of the book he also promises to analyse the dynamic aspects of
the problem,^ and he will probably succeed in illuminating these
obscure and intricate points, of which I for my part am far from
believing myself the master.

Our analysis is naturally valid for the construction of
machines. For firstly machines, the uses of which have not
changed, will be constructed to last long enough to be economically
remunerative, and secondly, if we are considering a change in
the life-time of machines, those machines which only last as long
as before will be given as many useful qualities as possible from
all points of view. This property, which Akerman deals with in
his Introduction, he sums up in the name ‘‘ automatism It is
well known that machine technologists talk of an automatic
power of 100 per cent and an automatic power of 50 per cent
according as machines save ” more or less labour. The author
deserves all praise for seeking to give greater scientific precision

^ [The second volume of Realkapital und KapiicUzins (Stockholm, 1924 )
deals With durable real capital in dynamic conditions.]

REAL CAPITAL AND INTEREST 271

to an idea wliicli is so vague in ordinary everyday speecli. Yet
ids treatment of the question does not seem to be as clear and
definite as would have been desirable ; if it is at all possible to
obtain perfect clarity in this sphere. He says (pp. 27~8) that
any durable capital-good, in the production of which some
labour has been invested, has thus attained a degree of
automatism such that it later requires a given amount of
co-operating labour, neither more nor less, if the maximum
amount of efficiency per co-operating labourer is to be obtained
Automatism, he continues, is to be regarded as high or low
according as the machine in question requires '‘a smaller or
greater amount of co-operating labour in proportion to the
labour originally invested, in order to reach this maximum return
per unit of co-operating labour

To say the least, this description is not very lucid. If the
words italicized (by the author himself) mean the free labour
resources co-operating with machines, as the context appears
to require, then the statement is incorrect. For whom would
it benefit that the product per unit of this labour and no other
should be as large as possible ? But even if by ‘‘ co-operating
labour ” we understand the whole supply of co-operating labour,
both free and invested, Akerman’s thesis still remains incorrect,
unless the rate of interest has fallen to practically nothing.
In equilibrium, the distribution of the available supply of labour
between free and invested labour must rather be such that the
capitalists obtain the maximum interest compatible with the
current rate of wages, and labourers, taken as a whole, the
highest wages compatible with the current rate of interest. But
in these circumstances ‘‘ Automatism ” becomes an integral part
of the whole problem of production, fcom which it cannot be
separated. Nor can it acquire an independent significance.
On the other hand, there ought to be no serious difficulty in
attempting a theoretical treatment of the question, in which we
start with a state of economic inertia, all machines being of
identically the same kind with reference to their potential uses.

The book is not without its shortcomings and weaknesses,
but as far as I can see they are fewer and less important than
one might have expected in the treatment of so extraordinarily
difficult and exhausting a problem. The normal reader cannot
imagine the practical difficulties encountered in carrying out the

272 LECTUEES ON POLITICAL ECONOMY

calculations. The unreality of the arithmetical tables is striking
enough ; for example, one cannot help noticing that they record
a precipitous decline in the rate of interest after a comparatively
modest increase in capital. Again, according to Table IV, when
a society’s capital increases there is an almost uninterrupted
fall in the total capital gains — & circumstance which, in this
respect, is very discouraging for capitalists. This result is largely
due to Akerman’s actual choice of the terms of the i-series —
the additional labour necessary for making a machine last longer.
If they are to correspond to the facts of the real world, they
should from the very beginning decline more rapidly than he
makes them do. It was impossible for convenience of exposition
to adopt this procedure, for in the author’s view the terms of
the iseries should be chosen so as not to infringe the principle
that in general the duration of some capital-goods cannot
advantageously be extended beyond certain limits. It is, there-
fore, not sufficient to make the terms of this series stop falling
at some point or other, but, as the author rightly mamtams
against Eae (pp. 22 and 118) it is also necessary that their
average size (per year of life-time) should cease to decline. If he
had wanted to obtain figures more closely approximating to the
real world he would, in the first place, have been compelled
considerably to extend the i-series. In the second place, the
tables would then have become too full, and it would have
necessitated the use of higher powers for the rate of interest
for a moment of time, and the calculations would have become
extremely tedious and difficult.^ Most of these obstacles might
be overcome by the use of more powerful mathematical tools,
but this must be left to the future. As they stand, most of the
columns of figures in all cases fulfil their function of illuminatmg
the most significant aspects of the phenomenon.

In my opinion, the more purely critical sections of the book
testify to Akerman’s erudition and soundness of judgment.^

^ The series employed are all recurrent and can therefore be reduced to a
few terms — a fact with which the author does not seem to be acquainted, except
in the case of geometrical series,

* I may mention m passant that the passages from my Uber Wert and
Lectures quoted on p. 135 are hardly inconsistent. In the earher passage
J am dealing with the antithesis between short- and long-term investment.
Akerman does not make this pomt clear. I maintained that arithmetical
averages are still of some use in handling short-term investments. 1 did not
say that this method was exact, for if that were so they would also be applicable
to long-term investments. I must express my gratitude for an acknowledgment

REAL CAPITAL AND INTEREST 273

I am convinced tliat on the whole the author has made a really
significant contribution to the theory of capital, and it is with
great interest that I look forward to the continuation of his work.
Only I should advise him to remember in his new exposition that
the contemporary reader, even of scientific works, seldom has
unlimited time and patience at his disposal.

of my own work whidi if anything is only too generous. He wishes to
associate my treatment of the Wage-Fund with Bohm-Bawerk’s well-grounded
Wage-Fund theory. Actually my more rigorously mathematical analysis of
Bohm-Bawerk’s arithmetical exposition was much too derivative to have any
particular merit of its own.

2. Real Capital and Interest (Contmued)

(6) A Mathematical Analysis of Dr. Akerman's problem

In the following pages, we shall attempt a mathematical
solution of the problem we have just been discussing.
We start with the assumption that production is continuous
and that capitalization takes place on the basis of the rate of
interest for a moment of time. Since machines are in fact discrete
and are not therefore capable of being divided into infinitesimal
parts, our result will of course only have an approximate validity.
But no more can be obtained by any other method of approach.

Using an amount of labour a, a labourer (or group of
labourers) produces a capital-good, e.g. an axe, which is instantly
taken into employment. If used normally the axe can remain
in use for n years after which it is devoid of any value. We
assume that the axe is so small (or that the group of labourers
required so great) that the length of time required for its production
compared with its actual life-time need not be taken into account.
Our calculations are thus simplified to a considerable extent
without, however, losing in force. Naturally it does not follow
that o is a negligible quantity If, however, a labour-year (or
else the work of a whole group of labourers for a year) is taken
as the unit for the services of labour, a becomes quite small

and its reciprocal ~ quite large.

The exchange-value of an axe to the man who buys or
employs it naturally depends on its utility for his purposes.
We make the additional assumption that this value is known,
and that it is estimated to be 6 (shillings) per annum ; b is there-
fore the sum of the undiscounted value of all its uses for one year.
Let us assume that the axe is applied uniformly throughout the
year (or years). If is a fraction of time, then the value of
the axe’s uses for this time is clearly b.At If we relate the

^ For example, , in modern house-building all the different parts and
accessories of the house are manufactured at the same time as the foundations
are laid, so that the whole house, even though actually requirmg an amount of
labour corresponding to ten labour-years, is in fact completed in the course of
a few months, perhaps only a few weeks, i e in a negligibly small period of time
as compared with the house’s own probable duration.

274

276

ANALYSIS OF AKERMAN’S PROBLEM

axe’s employment tkrougli t years to the present moment and
let r be the rate of interest, we obtain its present value by
dividing bAt by the binomial expression (l + r) raised to the
power t. Thus —

h.At

(l + ry

( 1 )

Let 1 4“ ^ where 6 = 2* 718 ... is the base of the natural
system of logarithms and p is thus the “ natural ” logarithm
of 1 + r, i.e. the ordinary logarithm divided by * 434 ... It can
also be expressed in terms of r by means of the logarithmic

series, p = loge(l+ r) = r -- - +

. which is convergent for

r ^ 1. p is the instantaneous rate of interest for a moment of
time, or what is called in German Verzinsungsenergie p and
r more or less coincide with sufficiently small values for r;
otherwise p is always less, if only insignificantly, than r (if r is
5 per cent, p = 4-88 per cent, and if p is exactly 5 per cent
f is 5 * 13 per cent, and so on). In each case they stand in a definite
arithmetical relationship to each other, and it is not very
incorrect to assume them to be wholly substitutable for
each other.

Substituting in this manner, we obtain for the value of
each of the axe’s uses discoimted to the present —

b.e-fi^At ( 2 )

Since i is to be taken here as continuously variable, we obtain
the present value of all the axe’s uses and therefore its own
present value by the summation (integration) of the above
expression between 0 and n, two points in time

b^e-P^dt =

(3)

(corresponding to the normal calcnlations for annuity-loans).
If r, and consequently p also, were so small that in expanding
the series for the exponential function —

g-pn =il — pn +

(pn)*

{pnr

etc.,

1.2 1.2.3

276

LECTUBES ON POLITICAL ECONOMY

we need only include the first two terms, the above expression
is reduced to in other words, the present value of the

axe is equal to the (imdiscounted) value of all its uses. If we

include the first three terms, we

J, i.e. the total

use-value discounted by simple interest on it for half its period
of use.

In equilibrium, the value of the axe coincides with its costs
of production. Let I be wages per head per annum. Then —

6 .

1

P

= al?-

( 4 )

This equation holds for a, 6, I, p (or r), and n, as they
are determined in an equilibrium situation. If equilibrium
is not yet reached, equation (4) describes the following conditions
instead. Let us assume that not only is b (the value of the
axe’s use for a year) given, but also p and r, r being taken as
the usual rate of interest current at the time. Now if n and a, the
life-time of the axe and the amount of labour needed for its
production respectively, were also to be technically given (as we
often take them to be), the E.H.S. of the equation would represent
the sales-value of an axe (i! the wages per annum multiplied by
a the unit of labour) which is received by the axe-manufacturers.
Now although the magnitude of neither n nor a is given, they
are technically related to each other. By investing more labour
on an axe we can increase its durability, all other properties
remaining constant ; n is thus a function of a and a of n, i.e.
of the period for ^hich it is sought to make the axe last while
it is being manufactured. Clearly, both increase together, but
n must increase more than proportionately to a, otherwise,
however low the rate of interest, labour could not be employed
in producing axes of longer duration, but it would be employed
in producing many less durable axes instead. We assume
therefore that a varies as a fractional power of n, i.e.

a = kn'' (5)

where is a constant and v a proper fraction. If, for example,
V a would grow proportionately to the numbers 1, 2, 3,

^ K the yearly services of a whole group of labourers — ^say of ten men —
is taken as the unit, the amount a m terms of this unit falls in proportion as I
(in terms of shillings) increases.

ANALYSIS OF AKERMAN’S PROBLEM

277

4, etc., whilst n grows as the numbers 1, 4, 9, 16, etc. In other
words, n increases geometrically in relation to a. Of course
the form of this function is too special to reflect the actual
relation between a and n when both are undergoing large changes,
but with smaller variations which, as a rule, are the only ones
likely to occur in practice, it may be as good an approximation
formula as any other.^ If we assume, for example, that it held
for axes lasting for 16 to 36 years, and that v = then the
constant k represents a quarter of the amount of labour required
to give the axe in question a life-time of 16 years ; or else,
and it here comes to much the same thing, a fifth of the labour
needed to produce an axe which is intended to last 25 years, etc.

At this stage, we could, of course, eliminate a from equations
(4) and (5), and then I and b would be the only unknowns
outstanding. But we prefer to retain both equations in their
present form.

For the labourer, or group of labourers, if they themselves
are the entrepreneurs, the most advantageous value of n is
that which makes the selling price of the axe a maximum
in relation to the amount of labour invested, i.e. makes I attain
its maximum.^ Since a variable magnitude at its maxima (or
minima) behaves like a constant, we have to differentiate equation
(4) as though I were a constant, which gives

be'^P^An = lAa.^ ( 6 )

We have again obviously obtained on the L.H.S- an expression
of the form of equation (2), n and An taking the place of t and
At, The obvious implication is that at its maximum bAn^ the
last addition to the value of the axe, when discounted to its
present value exactly corresponds to lAa^ the last increment
to the cost of its manufacture.

We get by logarithmic differentiation of (5)

Aa ^ An
a n '

1 On the other hand, there is no expression to correspond with Akennan’s
i-series, which would describe the condition that the durability of some capital-
goods cannot successfully be increased beyond a certain point. ^

* We might also assume that they do not sell their axes but hire thern^ out.
Here they must themselves borrow at the rate of interest r or (p) for maintainmg
them — ^the theoretical result is the same in both cases. ^

3 That the remaining condition for the maximization of 1, as of p in the
next case, is here always fulfilled will be shown later.

278 LECTURES ON POLITICAL ECONOMY
Substituting in (6)

= la (8)

V

and combining with (4), we obtain finally

eP» = 1 + ^ (9)

Tliis result is rather peculiar. The product pn is here the
root of an equation, in which v is the only variable. In other
words once the particular function we have used for extension
of life-time is taken as given, it follows that the product
of the rate of interest (with continuously compound interest)
and the optimal lifetime of the axe is a constant, independently
of the ske of b, as soon as we regard v as a technical datum.
Even with the choice of a less simple function, the connection
between n and p remains independent of b, provided a is a function
of n. (9) is of course a transcendental equation, but we can
easily obtain an approximate result for the larger of the real
roots.^ (The other == 0 for every value of v.) If, for example,
V pn is roughly 1*27, so that if p is *05 (and the ordinary
rate of interest therefore a little over 6 per cent) the axe’s
optimum life-time is always ctrca 25 years, however much the
value of its uses, calculated per annum, may vary. We shall
indicate this root by ^(v) with the proviso that it is a constant
as soon as v is taken as a technical datum. The following
analysis depends to a great extent on this result.

We have hitherto regarded the rate of interest (r or p) as
given. Now if we consider capitalists as entrepreneurs, I must
be taken as given instead. Those capitalists, who at a given
wage manufacture axes to be later applied, are confronted
with the problem of makmg the axes last so long that the capital
invested in their manufacture receives the maximum rate of
interest. From a mathematical point of view, this problem
leads us to exactly the same formula as the first, for when
p reaches its maximum, it behaves as a constant, and we have
therefore to differentiate equation (4) as though I and p were
constants. We obtain precisely the same equation as before,
and also equation (9) in a similar manner.

^ This can be solved by expanding according to Lagrange^s theorem, taking
out the root pn = 0.

ANALYSIS OF AKERMAN’S PROBLEM

279

= 1 + -^ (9)

But it is no longer p but I wMcb is the datum. To find n we
substitute in (8) the value discovered from (9) for pn = ^(v) (e.g.
1*27 if V =i), and eliminate a by means of (5). Thus

wi-” = ^ Ave^fr), (10)

or wbat comes to the same thing, as <f>{v) is the root of (9).

^ jfe[v + 4{v)] (10 bis)

If v ==f and <f>{v) — 1-27, we get

V'«==t1-77A

b

We are here restating the principle with which we were acquainted
before, that an increase in wages produces a tendency to increase
the durability of a capital-good, in this case in geometric
proportion to the rise in wages.^ This tendency corresponds
to the extension of the period of production in the case of
‘‘ variable real capital ’’ (circulating capital).

Before going any further, we should like to mention an
interesting fact with reference to the average investment-period
of capital tied up in a particular capital-good. Under normal
circumstances, the annual yield of a fixed capital-good will
afterwards repay as well as yield interest on the costs incurred
in making it. we ha^^e maintained in our review of Akerman,
the question of the order in which either the former or latter
occurs is of merely formal interest. But we should be able to
represent the average investment-period of this capital as
a period such that if all the Uses of the capital-good were finally
turned out at the same time^ they would yield the same interest
on the capital as the owner actually obtains. Let this period
be m. Since in our example the total value of all the uses is
clearly 6.n, with equation (4) we get

hne^p^ = 6^^ = aX (11)

P

1 We shall later try to show that this result is perfectly g^eral, quite
apart from the function for extension of lifetime.

280 LECTDEES ON POLITICAL ECONOMY

if a is here increased, and therefore according to (5) n too,
m must also be increased.^ Now since w is at its optimal
value and we can regard Z and p as constants (for one is
assumed to be an actual constant and the other has attained its
maximum), we obtain by logarithmic differentiation of (11) the
equation — '

An Aa

— (12)

describing the relations between the simultaneous increases in
TO, m, and a. This result is not difficult to interpret. Since a is

the amount of labour required to produce one axe, ~ is the

number of axes produced by one unit of labour * and - the

a

number of (potential) yearly uses of ^ axes. Therefore — is

the value of all their uses. If for the moment we call this
expression P, and retain our assumption that b is a constant
we obtam by logarithmic differentiation—

AP _ An Aa

th« “ «aortu«tion period ” |. But the W the rate of interest, the more

closely does it approximate to |. Sinee p the rate of interest varies inversely

SLps“ve^r^^*X” “t the same time as

of the fact that compound mterest is^u^nor f n another example

tion ; for with the ordmary ammitv-loa^lonlAf^-^^ P^poses of computa-
amortization period sometimes falls short of j.o]f
times exceeds it, according to l ling loan-period and somt

If, for example; a man has to S i^^^rest.

year for the next twenty years the best £50 at the end of every

whole lot at once after thf do would be to pav the

not otherwise.) ^ “ above 5 per cent; but

J Since a is small, ] is large. But to make matters more intelligible we

axes ca^be prodn^'’rimort*ri^^!^eo^ ^so^Vi^ *7
be r^arded as a single oapit^ood. together they can

ANALYSIS OF AEERMAN’S PROBLEM 281

p= Am . (13)

P

We miglit have derived this result directly from (11) ; it holds,
therefore, even if 6 is not taken as constant, but is allowed to
vary in some proportion or other to the lifetime of the axe, as
soon as p or Z attains its maximum. Thus in dealing with fixed
capital we obtain a counterpart to tlie Jevonian principle that
interest is “ the rate of increase of the produce divided by the
whole produce or is the marginal productivity of waiting
i.e. with reference to average waiting reckoned according to the
above principle. At this point we must note that the amount
of labour invested is taken as fixed (=1 unit of labour) so that
the average period of waiting becomes capital’s only variable
dimension. It is also worthy of notice that the principle holds
for the whole duration of the capital-good, and not merely for
the period for which the stock of machines of different ages
(= the existing fixed capital) stiU has to last. On the other
hand, it is fairly clear that our principle is completely independent
of the assumption we made about the form of the function for
extension of lifetime.

We turn now to consider the stock of fixed capital. If
the labourer (or group of labourers) continues to produce axes,
1 . n ,

he (or it) will produce - axes in one year and - axes in n years.^

Within this period the number of axes in use will obviously
continually increase, but once we get beyond n, it ceases to do
so, since the oldest axes are discarded pan fossu with the
manufacture of new ones. Thus we have got here & fixed capital
consisting of axes, which is ‘‘ staggered ” in structure and which

includes ~ axes of various ages, and as a matter of course the
a

nurriher of uses availahle is the same cU any rnornent. The total
(undiscounted) value of all the uses available in one year is

^ The expression - has thus a double significance ; it is the amount of

potential uses of the number of axes produced by one unit of labour in the
first place, and the total number produced by a labourer in n years in the
second. Because of its second implication it is described in the text as the
total number of uses available at one and the same time.

282 LECTURES ON POLITICAL ECONOMY

& ^

therefore Again, the total value of all the potential uses

CL

which the fixed capital, consisting of axes and existing at each
moment, represents, is clearly

n n

6— — = Or-

a 2 2a

For the time elapsing during the manufacture of an axe
is assumed to be so short that the age of the axe grows
continuously from 0 to w years. This proceeds on the assump-
tion that only a single labourer or group of labourers is employed

in producing axes. If, however, M labourers or ~ groups

of labourers with ten men in each group are occupied in
manufacturing axes, all our quantities will naturally have to
be multiplied by M ; from now on we take the annual services
of one labourer as the unit of labour.

Now in order to find the value of the capital itself we employ
in our calculations that rate of interest which is attained when
the best possible line of action is adopted in the use of each
individual axe for the whole of its life-time. Once equilibrium
is finally reached this rate must coincide with the current rate.
According to (3) the value of a new axe with n years to live is

Ifi L, Therefore the residual value of an axe already

used for t years must be

6(1

(14)

Since At is an infinitesimal period of time we regard the axes
between the ages t-\- At having the same value. Now since

one labourer produces ~ axes per xmit of time (one year) and
a

M

M labourers therefore produce — azes ; the number of azes in the

a

moment At produced t years ago is
standing value is according to (14)

AtM

and their total out-

1 — ,

M At.

a p

iUSTALYSIS OF AEJIRMAN’S PROBLEM 283

Summing all these values, we obtain the value of all the fixed
capital by integrating between < == 0 and « = ». Thus

n

Z = M- - I (1 - e-(»-<)p)d« = M- P” - ^ + (15)

^ pj a

a '

This equation corresponds to the sums of the recurrent series
in Akerman’s analysis, which he does not however summate.
It ’can be checked, for if pn is so small that we need
only consider the first three terms in the exponential series

e P = 1 — pw + + etc., our equation is then

reduced to M~ — , corresponding to the undiscounted value of
a (h

all the potential uses of the axes, as we have already seen.
Even if the fourth term is included, we obtain the same expression

multipUed by the binomial (l --y), i.e. the value of all the

potential uses minus the simple interest on them for a third, of
the whole lifetime of each axe — a, new but naturally incomplete

approximation. The quantity -r is the distance of the centre

o

of gravity from the base of a triangle, the height of which is n and
the base the number of axes in existence. If the potential uses
of the whole existing stock of axes are discounted back to the
present, the average period of discounting should in fact be
n ,

- (cf. review, p. 270), if we use simple interest.^

^ If a capital-good lasts altogether jV' wmlca, and if the same number of
capital-goods are all of various ages, the number of remaining weeks’ uses of
a good already in existence for T weeks is clearly N—T, and its average period

N—T

of discounting, using simple interest, is — ^ — 'W’eeks. We obtain the average
period of discounting for the whole stock from the formula : —

27

i

{N - T)^

27 (N--T)

T^O

^ 1)« 4. _ . + 9 4, 4 -f- 1)

N N •• -

2zV+ 1
6

N

or since N is here a large number, ^ weeks approximately.

And in the same

way, still using simple interest, we get the average period of investmeni for a
“ staggered variable real capital ”. (Of. the relevant passages in my review.)

284 LECTUEES ON POLITICAL ECONOMY

We can easHy prove that at any moment the net value of
the uses of the whole of the axe-capital, i.e. the gross value
mmus the cost of renewal of capital, is the interest on the total
value of the capital at the same moment. For it foUows from what

we have just said that the former is m{^— ^ At, which, using
(4), becomes

a

on — 1 +

At = pKAL

(16)

(16) is of course bound up with the fact that the residual
capital-value of the axes already in use is precisely estimated
accordmg to this rate of interest, and may therefore be called
a truism.

We have not yet made any use of our assumption about the
nature of the Action of “ extension of lifetime ”, i.e. equation
(5). 0/ice (5) is token into account, K, the amount of capital
becomes a much simpler expression, for in this case pn is a con-
stant = ^(y), and so the numerator of our fraction also becomes
a constant. Further, p and a can be simply expressed in terms
of n, so that we can express K in terms of M, b, and n. Since
accordmg to (10) n is proportional to some power of the ratio

j, we can express K in terms of I and b only, but always with

the proviso that it is also a multiple of M and includes a constant
factor, which is solely dependent on the value of r, which is

techmcally given. The significance of this consideration will
become apparent later.

in ac^l tact neither I noi b is given, but the value of
boto 18 ultimately determined by the co-operation of free labour
with real capital m the production of commodities. For we
1^!Z^ wmpetition wages I are the same for all

flke^? “replacement labour”

( nnan), which is annually mvested in machines. To obtain

whnl necessary for solving the

S aU assumption

onl! pf the community consists exclusively of

oT./lH’!q ? capital-good, in this case axes, and that only
one kmd of product is produced. Since we have previously only
been occupied with capitolistic production in its simplest fon^

ANALYSIS OF AKEEMAN’S PROBLEM 285

we are doubtless justified in making an assumption wHch is
ratlier fantastic if taken by itself.

Let X free labourers co-operate with y tmits of capital (axes)
in a given form. Now with the optimal employment of resources,
the product, or the value of the product, will clearly be 2i,fun<Aion
of both X and y. We can decide a jytion that this function
must be homogeneous and linear, i.e. such that a uniform
increase in x and y produces exactly the same percentage increase
in jbhe product. For if two labourers, each having his own axe,
could together produce more than twice as much as one labourer
with one axe, or if the product of three labourers and three axes
was proportionately even more, and so on, then we should
obviously have to let the labourers co-operate in groups in such
a way that the maximum efficiency was reached. But once this
maximum has been attained, a further increase in labourers and
axes, i.e. an increase in the number of such groups, would only
produce a proportionate increase in the product. On the> whole
we can therefore assume that with a constant stock ’’ of axes
per labourer, the product grows in proportion to the number
of labourers, but with an increasing or diminishing stock of
axes, labour remaining constant, the product certainly increases
or diminishes in some degree, although less than proportionately
to the change in the number of axes. In other words our
productivity function, which we represent by F{x, y), must take
the form,

F{x,y)=x0(^,

y

where ^ is a function of a single variable, i.e. of the ratio

X

It increases or diminishes simultaneously with its variable,
but to a lesser extent. For if it increased in the same proportion,

y

the whole expression could be reduced to cx- = cy, where c is

a constant ; in other words, we should arrive at the ludicrous
result that the product was solely dependent on the number
of axes and not at all on the number of workers. We should
get a still more ludicrous result if the function 0 increased
more than proportionately to its variable.

Since we are chiefly concerned with expressing this relation

286

LECTURES ON POLITICAL ECONOMY

in as convenient a form as possible for our calculations, we
may simply let tbe 0-function vary as a root of its variable,
i.e. we may put

F{x, y) =

where a and ^ are both positive fractions and their sum = 1.
P, the value of the product computed for a moment of time,^
thus becomes

P = F{x, y) = cxPy?, (17)

If this equation
y, we obtain

is partially differentiated with respect to x and

dx ^

P

a—

X

and

dy ^ ^

Let us postulate a stationary state in which there is perfect
competition between employers and labourers. Once equilibrium
has been reached, the first partial derivative must necessarily
equal or I the wages per head per annum, and the second 6,
or the payment received for the yearly use of an axe. Thus

P P

i = a— and h = j8— ,

X

(18)

from which, among other things, it follows

^xl + yb ^ {a + P)P = P, since a 4- j3 == 1.

In other words payments, so determined, made to the labourers
and the owners of the axes, will together absorb the total value
of the product ; which is as it should be. Similarly, assuming
a continuous productivity function, we obtain the simple ratio
of h to t —

(19)

b ^Px
1 ay

Let A be the total number of labourers or the supply of
labour annually available. If Af is the number of labourers

^ We might also have calculated it for an infinitesimal period of timef
i.e. multiplied both sides of the equation by At, But once production is taken
as stationary, this procedure would make no difierence whatsoever.

ANALYSIS OF AKERMAN’S PROBLEM 287

always employed in the manufacture of axes in order to renew
or maintain the fixed capital consisting of axes, then the amount
of free labour is plainly A -M. It follows that the number

of axes in use at the same time is ~ and that in equilibrium

just this proportion between free labourers and axes employed
must obtain in each firm, as the result of reciprocal supply and
demand , otherwise some of the labourers or axes would be

unemployed. We can therefore substitute A ~M and — for
, . . a

a; and y m our previous formulae, and replace P by n, the value
of the whole social product. Thus we obtain

n = c(A- M)<^M^Qy (17 })is)

and

(18 M

and

b p A -- M a

By making a simple ckange in equation (8) and tken combining
it witb (9), it follows that if the most profitable lifetime is
attained for every axe, then

b a

^ = veP^ ^

I n

n

= (y + ^{y))~ (8 bis)

n

where <f>{v) is the root of (9).

We finally obtain —

( 20 )

This result is calculated to create some astonishment. All the
magnitudes on the E.H,S. are constants irrespective of the
amount of social capital. These constants reflect the assumptions

288

LECTUEES ON POLITICAL ECONOMY

we made (1) for tlie tecbnical conditions under wkich onr
capitaLgoods are manufactured, and (2) for their co-operation
with free labour in the production of consumption-goods. Our
assumptions have thus shown that, however much the amount
of capital itself changes, the distribution of the existing supply
of labour between free labour co-operating with capital-goods
and labour employed in the maintenance or renewal of capital
itself^ remains unchanged. And yet only within limits, since
the form of our function is too special to be valid beyond a certain
field of variation, even if it contains one arbitrary constant.^
Within these limits, however, capital, when it does grow, grows
exclusively in height and not at all in breadth. N,B , — When
capital first increases and there is a consequent disturbance
of equilibrium, capital will also — or rather exclusively — ^grow
in breadth, since in the beginning the additional number of
new capital-goods will be of the same tj^e as those already
in use^ If, on the other hand, the amount of labour invested
per moment of time is temporarily increased and the amount
of free labour diminished, there will be a rise in wages and a fall
in the value of the use of capital (axes), more or less in this
sequence. Further, according to (10), the new capital-goods
now produced will be manufactured to last longer, as this method
of investment has become most profitable. But when equilibrium
is reached once more the amounts of free labour and of labour
engaged in replacing capital resume their former proportion
(at the same time the labourers lose part of, but not all, their
recent increase in wages and the capital-goods regain part of,
but not all, the value they' have just lost). Employing this
interesting result, we might regard the prodv..ctivity function
and the function for “ extension of lifetime ”, which have
been selected, i.e,

a ^f{n) == kn?'

and P == F{x, y) = cxf^yP (a + j8 = 1),

as typically mrmal functions from which, taking them as the
simplest elements in the problem, we must start in the analysis
of the more complicated phenomena of the real world.

^ In a stationary state these quantities will themselves be constant.

* The two coefficients h and c refer only to the value of units, and therefore
leave no room for varying conditions in other respects.

ANALYSIS OF AKERMAN'S PROBLEM. 289
With these constants, the values of M and A plainly become

.and^-Ai= +

Af =

, (20 bis).

a(y + <f){y)) + ^ a{v + <f>{p)) + jS

Let V = I : then (f}{v) =1*27. Further, let a = Then

M = -^, A-M = —Ia.

2-77 2-77

Rather more than a third of the existing supply of labour should
therefore be engaged in manufacturing axes, and the remainder
— ^about two-thirds — ^in the application of the existing stock of
axes for the delivery of saw-logs. This result we achieve without
taking the amount of axe-capital into account, for, with a small
supply of capital in the form of axes, as long as our assumptions
hold, they must necessarily be manufactured so as to last for
a correspondingly short period, and will therefore need renewal
all the more often.

M being determined, the whole problem can be solved
without any further difficulty. The remaining unknowns are
(1) the amount of capital expressed in terms of the product
or of money (for the price of the product is taken as fixed on
the great staple markets), (2) the product per annum in terms of
the same unit, (3) the duration or lifetime of the capital-goods
(axes), (4) wages per annum, (5) the value of the yearly uses of
an axe, and (6) the rate of interest prevailing in equilibrium
and current throughout the economy. It does not matter which
of these is taken as the independent variable, for in any case
all the other quantities vary as certain powers of this parameter,
each being multiplied by it^ own constant co-efficient. If we
choose n as our independent variable, i.e. if we imagine an
equilibrium situation where the total period for which the
capital-good lasts is n years, and let C^, Cg, etc., be the constant
coefficients, we obtain

K — TT =

I == h =

and, as before,

p = 4>(v)n-^.

^ It follows from this second, assumption that capital and labour are equally
important in production, so that a percentage increase in one factor hj^ the
same effect as an equal increase in the other, which of course is only conceiyable
in a special situation.

290

LECTURES ON POLITICAL ECONOMY

It follows immediately that the exponentials are solely
dependent on v and ^(= 1 — a). The coefficients depend on
k and c, the meaning of which is well understood. In addition,
Cl and C 2 , the first two coefficients, contain A as a factor ; for
by dividing by A we had obtained the capital and product per
head (of labourers) of the population.

Thus with the simplifying assumptions we selected the
problem is now solved. But we must of course be very careful
in drawing general conclusions from the results obtained if only
because of the above reservation (and quite apart from the fact
that they are no longer applicable as soon as our quantities
move in a negative direction, for what is not valid in a special
case is still less so in the general). But a few observations may
still be permissible.

As y is < 1, the capital K clearly increases simultaneously
with n, and conversely n with K. For the reason mentioned in
our review, this interrelation must be general. Similarly, tt grows
when n (and jS”) increase, but much less than the latter, since
the index is smaller by one whole unit.^ The conclusion that
an increase in fixed capital also produces an increase in the
annual product should also be perfectly general, independently
of our particular assumption, as we shall immediately attempt
to show.

Similarly, I increases when n and K increase, but 6 diminishes
when n and K increase. This conclusion ought also to be general
in its validity, as we shall soon show.

Since the expressions for tt and I have the same index, the

ratio j remains a constant, in other words, with increasing
i

capital, wages remain an unvarying part of the increasing product,
which is a necessary consequence of our assumptions. Given
our particular productivity function, the sum of the wages of
free labour in each firm and throughout industry constitutes
an unvarying portion of the product, which follows from (18) and
(18 his,) And besides since, according to our function for the
“ extension of lifetime ”, A -- M, the total number of free
workers remains constant, every free labourer (and therefore

V = i and p = I, K becomes proportional to but r only

to ^n.

ANALYSIS OF AKEEMAN'S PEOBLEM

291

all labourers) receives a constant part of the national dividend
when capital increases (though of course labour now invested
is paid in consumption-goods which are ready tiow^ and not in
the consumption-goods which they themselves help to make).
Naturally, this conclusion cannot be general.

If the proportionate share of the labourers in the total
national dividend is constant, then the capitalists’ share is
also constant. But, as we have maintained, this result holds
for the interest on all the capital at the moment of time in
question, if the rate of interest is p.

Hence

KAt

rrAt

must be a constant. This result is correct,

for

K G

p— = since the powers of n cancel out.

IT 62

It may be added that the number of capital-goods (axes)
in use at the same time, which on the above analysis is

M- =
a h

necessarily increases with n and also with JT, although in a smaller
proportion than either, since 1 -f- ^8(1 — = 1 — a(l — v) -f 1 — *

> 1 — V. This result is general and holds as we shall soon
show, even in the exceptional case when M diminishes with an
increase in K.

Let us turn to the transition from one equilibrium to another.
It is now possible to discover to what extent the closely-related
proposition originally advanced by von Thiinen that the rate
of interest corresponds to the marginal productivity” of
capital is corroborated by our formulas in the modified form put
forward by Akerman. By logarithmic differentiation we obtain
directly

AK An , Att ,An

(1 + )S(1 - v))— and — = ^(1 — v)~

K

Therefore

n

n

Arc /8(1 — v) rr

iS(l -v)K

We can easily express the value of the ratio — without needing

to bother about the rather complicated constants Ci and
Since the share of capital in the product is equal to the interest

i;— !

292 LECTUEES ON POLITICAL ECONOMY

on all the capital = pK (cancelling At out), it must clearly
be TT — Al, or, if we take (18 bis) and (20 bis) into account, it is

^(v + <^{y) - 1)

V + j>{v)

Thus we obtain

7T V ^(v)

K~^{v + <f>{v) - 1)^’

and finally

Aw 1-v v + <f>{v) ■

AK l + ^{l-v)v + <l>{v) - V' ’

Out ratio is therefore proportionate, but not equal, to p. If

V = h 4^{^) = 1*27, and = a = it becomes *92^ approxi-
mately, i.e. rather less than p. This discrepancy is only to be
expected, when the increase in capital is partly absorbed by the
resulting increase in wages and only part of it is effective in
raising production. But since this explanation does not hold
here, we may infer that the principle is not general. If ^ is
quite small, i.e. if the capital-goods have only a minor significance
for production as compared with free labour, then as long as

V = the first fraction approaches 1 — J as closely as

1*77

possible, whilst the other is always — i.e. > 2. Strangely

enough, this ratio is thus greater than p.

In these circumstances, it is already obvious a priori that
von Thiinen's thesis is no longer verified, even in the form in
which Akerman proposes to recast it. In his analysis on p. 152,

Akerman starts by replacing the divisor AK by AK K

Al

and thus subtracts that part of the increase in capital absorbed
by the rise of wages. This method of approach is perfectly
justifiable (cf. my review) for Bohm-Bawerk’s thesis, as we can
see from a simple inspection of the formulae on p. 113 of my
Tiber Wert, etc.^ But in this particular case, it does not hold good.

1 If JZ is replaced by dZ - Zj in the equation at the bottom of t^e
pa^e, p. 113, op. cit.,

Ap'dt __ 2p'dt 2p'

dK ldt-\-m

t^p"' disappears from the denominator in the fraction on the extreme right,
which is reduced to = z (the rate of interest).

ANALYSIS OF AKERMAN'S PROBLEM

293

We obtain witbout any difficulty

Al rAK Al\

K-

and if J 77 is divided by this expression, tbe new ratio can be
written as

/Att

\ 77

An\ rr

77

n

)K -

(1 — v)(v 4- (f>{v))

(23)

The new ratio differs from the old only in this respect, that the
factor in the denominator depending on ^ drops out. Since this

Att

is always > 1 as also in this case, the new ratio is always

greater than the old one, but it is not therefore equal to p.
On the contrary, we should be in a position to show that it must
always be greater than p, except in both the limiting cases,
where either v is very small and np — ^{v) is therefore very
large, or where v approaches unity and (f>{v) tends to zero. In
hoik these cases the R.H.S. of the equation is reduced to the
value of p ; this is self-evident for the first case and can easily
be proved for the second by the method of limits.^ I cannot
enter now on the explanation of this very puzzling formula ;
presumably it belongs to the sphere of “ dynamic theory,
where we cannot confine ourselves to the comparison of two
different equilibria, but must also study the transition from
one to the other.

Finally, I shall tackle the question which really constitutes
the starting point for the whole of this fragmentary essay. It is
the validity of the principle that an increase in capital (measured
in units of product, or the value of the product remaining
unaltered) must, as a general rule, always produce an increase

^ Let V = 1 — € where € is a small positive fraction. The value of ^(v)
then approximates to 2€, and the value of the denominator thus becomes 4- €.
The denominator cannot change signs between the limits v = 0 and ^
smce it would be at a minimum between these points, which ^ can easily be
proved to be impossible. Therefore it always remains positive. We can now also
prove that this quantity v -f ^(v) — 1 always has a sign opposite both to the
second derivative of I with respect to n, p remaining constant, and to the
second derivative of p, I remaining constant, when their first deri’s^tive
becomes = 0 , whence the values of I and p respectively, obtained above,
always describe a real maximum. This ne^ not hold in the general case
(vide infra).

294

LECTUEES ON POLITICAL ECONOMY

in the volume of production. We have already seen that it is
valid on our assumptions.

But even this conclusion now appears more complex to
me than I had first believed. The proof I shall advance rests
on the assumption that a rise in wages relatively to the use-value

of the machine, that is to say an increase in always brings

about an extension of lifetime whenever such an extension can
be profitable (in other words if all the data are taken "as
continuously variable). According to (10) and (10 his)

but this conclusion follows from a = in*', our function for
* extension of lifetime If instead we take a more general
function, a =f(n), of which it is only assumed that it becomes
zero when n is zero, and increases more slowly than n, then
the matter is no longer seK-evident. Eor brevity, substitute

We now obtain the corresponding changes in x and n

by differentiating (4) and (6), which hold simultaneously

for a given value of a? when p has reached its maximum.

b

Thus —

I ^pn I

=t/(«) = (4 bis)

P 0

and also

e-pn == xf\n), (6 bis)

where/'(n) is the first derivative of /(n). This expression should
now be differentiated with respect to n, x, and p, for it involves
a shifting of the maximum points themselves. Let f"{n) be

the second derivative of f{n) and let = p and = ?•

Then on eliminating Jp, we obtain

n

ANALYSIS OF AKERMAN’S PROBLEM 295

Clearly, on our assumption {f{n) = 0 wlien n = 0 and

f'{n) di minis hing when n increases), p must be < ~ and q <z0.

n

The expression p is therefore always positive, and in the

numerator and the denominator of the next fraction q and
p — — are both Tiegative, But we cannot presume without further

analysis that they are simultaneously < or simultaneously
>py It is therefore not a priori impossible for Ax and An
to have opposite signs. Let us return to our function a =f(n)

= Then clearly p=z^ and q ~ — Y: Consequently,

n n

the numerator and denominator are here identical (if multiplied
by n they both become pn v — l=v + (j>{y) — 1) and our
equation is simplified thus —

X

= (1 - v)~,

An n

which can be directly obtained by logarithmic differentiation
of (10). Now since /(n), whatever its actual form, has the same
general form as our special function, we may infer even now
that X and n vary approximately to the same degree. But it is
not impossible that they might sometimes vary in different

^ But it can easily be proved that the denominator p + p — - is always

n

> 0. From (6 bis) and (4 bis) we find that it must here always have the vahae

g— -j- pw — 1
71(1

The denominator of this fraction is certamly > 0, and so is the numerator,
since its value becomes =0 for pn = 0, but later rises continuously, as

“ e -f 1 its derivative (with respect to pn) is always > 0.

It is impossible to get any further without knowing something about
p + g'. Still we can easily show that the inequality p q > 0 (which for

f{n) = kn^ becomes ^(v) + v — 1 > 0) constitutes the secomd condition
necessary for the emergence of a maximum value for I ot pin the general case.
This condition, however, need not be satisfied throughout. As far as I can see, if

^18 given and n is increasing, there is nothing to prevent a sequence in which

there first emerges a maximum value for p, then a minimtim, and then a
maximum again, and so on. An interesting consequence of this phenomenon
will soon be mentioned.

296

LECTURES ON POLITICAL ECONOMY

directions, from wMch it plainly follows that x{= and n are

b

not uniquely determined by each other but that x may have
two (or more) values for the same value of n or, conversely, n may
have different values for the same value of x.

In actual fact this last possibihty may often be reached,
but it should not on that account give rise to any serious dilemma.
The only practical significance it can have is that an increase
of capital is sometimes distributed between two different
investments — ^two types of machine of different durability
(though otherwise identical), both yielding the same maximum
return on capital. We have confined the number of different
investments to two^ because for technical reasons it often does
not pay to manufacture capital-goods lasting for intermediate
periods.^

It would have very much more serious effects on the following

proof, if two different values of x could hold for the same

value of n. But fortunately this can never haf'pen. If it could,
the conditions of our equations (4 bis) and (6 bis) could
simultaneously be satisfied for the same value of n with two
different a;-values, x^^ and x^, and with concomitantly different
values for p, and (pi > pa). In other words we should

1 e

obtain at the same time first = x^ f(n) and e ==

Pi

and secondly = x^fin) and e'^P^^ = x^f^n),

Pt

from which dividing we should obtain

^ li p has two maxima (as distinguished from a minimum) for smtiU
values of ~ the manufacturer of machines naturally chooses the larger^ which
we shall assume corresponds to the smaller value of n.

Were capital and ~ to increase, the maximum corresponding to the higher

value of n may become the greater. Now when p has two equal maxima (for
different values of n), there must be a case in the transition period analogous
to that described in my Lectures, p. 163. For a time the increase in capital
IS divided between two different mvestments, in which I and b and their ratio

- do not undergo any further change ,* for since an ever-growmg part of the

capital is successively transferred to the longer investment, M is dimimshed
and A-M increased, so that the proportion between free labour and the available
uses of the machines remains unchanged. But I have not been able to complete
any research into this mterestmg question in detail.

ANALYSIS OF AKERMAN’S PROBLEM

ePi>^ — 1 £p2,n — 2

297

or

Pi

Pi

Pi- P2 , Pi

o '

, Pi® - Ps®. , .
— ” + — 24 “ +•

If the values of n and p are positive, all the terms in the series
are also positive, and our assumption therefore involves something
absurd.

We may, consequently, proceed on the assumption that an
increase in always produces an extension of the lifetime of

capital-goods, even if this extension does not always occur
continuously ; at times it may take place in jumps (or more
correctly in such a way that capital is distributed among capital-
goods of the same profitability but of different durations).
On this hypothesis the proof of the thesis we previously
advanced takes more or less the following form.

When real capital increases it must always increase in
height ‘in so far as an extension of the durability of machines
is technically possible. For were it only to increase in “ breadth
so that the only effect would be an increase in the number of
machines of the old type, the labour permanently engaged
in maintaining it would clearly have increased, once equilibrium
had been reached. Hence it follows that the amount of free
labour would have diminished at the same time as the number
of capital-goods had increased. This must clearly result in a

shifting upwards of y in which case we must infer from our

conclusion, which we have just shown to possess general validity,
that an extension of the lifetime of the capital-good becomes
profitable. On the other hand there is no need for an inevitable
increase in the ‘‘ breadth dimension of capital which follows
from what we have said above. On our formula, with an increase
in capital the amount of labour required for renewing capital
should generally remain unalteired. We may therefore summarily
assume that an increase in capital may very well occur with an
accompanying fall in the breadth dimension. None the less
even in this case the number of capital-goods in existence aJt the
same time will have increased, for if it had diminished, since

298

LECTUEES ON POLITICAL ECONOMY

the amount of free labour has now mcreased, would have

0

shifted downwards and we cannot describe the position in which
n has a new and higher value as an equilibrium one. It therefore
emerges that there will be a larger number of machines
simultaneously with a larger supply of free labour, which must
obviously lead to an increase in the total product.^

Let us now take the com m onest instance in which machine-
capital increases in breadth as well as in height ; then the
amount of free labour will dimmish. We can conceive of this
change as occurring in two (or more) stages. Let capital grow
in breadth to begin with and only later in height also — ^in other
words, we first increase our M, n remaining constant, and after-
wards n as well (with M constant).

The first part of this procedure is soon explained. For since
the composition of machine-capital remains the same, the whole
process can be regarded as though M units of labour invested
m a certain way co-operated with A — M free labour in each
case. If M is increased, and A —M diminished by one unit,
then, ignoring infinitesimal quantities of higher orders, the
total product is increased and there is a difference between
the marginal productivies of invested and free labour. This
difference must be positive, for as we have always regarded the
Productivity Function as being homogeneous and linear (or that
it has again become so after any change has taken place) the
marginal productivity of each group necessarily coincides with
its wages. These must clearly be greater for invested than for
free labour, as the wages of the former also include sorm interest.
Now let the lifetime of the same number of capital-goods increase,
M remaining constant. Then it follows that the number of
machines in existence must increase (for the number of machines

per labourer working on machines is - = ) and, i£ the

ah

amount of free labour is constant, the total product must increase
still more. If the increase in machine-capital is such that as
far as the first part of our analysis is concerned the rate of

^ Similarly, if we abstract from technical discoveries, which change
f{n) and F{Xf y) the basic functions themselves, wages must always rise with
a relative increase in the amount of capital. The general character of the
Productivity Function plainly involves the result that I and b always vary
inversely ; if I has increased n must also increase.

299

ANALYSIS OF AKEEMAN’S PROBLEM

interest not only falls but is at the point of becoming zero, we
simply stop at this point and allow n to grow until the rate of
interest reaches its maximum (and becomes therefore > 0), and
using this point as our starting-point we begin again with the
same procedure.

Thus the net result is that a growth of capital, as long as
it is such as to be profitable, is always accompanied by an
increase in the total product. Consequently the paradox fall
irk the national dividend resulting from continued saving and
capital accumulation does not apply to perfectly free competition,
but the possibility of its holding for a situation in which capitalists
combine cannot be excluded.

So far we have treated the lifetime of capital-goods as if
it were altogether separated from their other property — their
Automatism as Akerman calls it. Actually, these properties
are scarcely ever independent, greater durability is normally
combined with greater efiiciency in other respects. We ought
to be able to express this mathematically so that the a-fnnction
does not actually have the simple form f{n), but also contains
a quantity as a variable which objectively refers to the ej0S.ciency
of the capital-good in question. Thus if, for example, g increases
from gi to g^, and ^2 = ceteris paribus we get a machine
of a new type, which can replace two of the older machines in all
respects. We need only substitute /(n, < 9 ^) iot f{n) in equation
(4 bis), and partially differentiate^ with respect to n and g, to
obtain a new equation corresponding to this variable. However,
I shall not undertake it here, as I have already taken too
much space.